I agree that "illicitly poached" is much too strong. But I have far less objection to "strongly influenced by".
It is probably a reference to unitarianism, which appeared circa 1500 and gave a public face for disseminating ideas that the trinity arose from Egypt for the sake of pursuing their own anti-trinity party line with a strawman on hand they can pull out of the carpet bag.
Late antiquity was a time of great eclecticism, when ideas from all over were coming together in a mutually influencing mix.
Whatever was there of eclecticism of late antiquity owes its heritage to the ecclecticism of classical antiquity by the romans. Despite having a sprawling empire, acceptance of the Roman Pantheon at the express exclusion of all others was not the price of membership. Sure, there was a high standard of political affiliation, but there was a broad acceptance of customs and beliefs of different cultures.
The roman empire was like a thread holding a string of pearls. When that string snapped, you had various groups grabbing handfuls of them, which lent itself to a sort of threshing out of ideology that the Romans had staved off for many centuries ... kind of like a massive overbearing schoolyard bully ushering in an era of conformity due to their capacity to thump any insurgency into submission.
There had long been a fondness for triads in traditional mythology and in rational philosophy, I'm not sure why. That's certainly true for the Neoplatonism that was so influential at the time when the Trinity doctrine finally crystalized.
Tracing the "threeness" of the trinity seems to more hellenistic than hamitic. I guess you can go one better, and try suggesting that the greek notion of three arose from egypt, but even that tends to say more about why the greeks were expressly accepted (and the ancient Egyptians expressly rejected).
Early Christianity didn't exist in a vacuum, influenced only by Hebrew scriptural tradition and by the New Testament.
What all the abrahamic religions lacked was a philosophical tradition (which they inevitably hijacked, in subsequent centuries, from southern europe). IOW the missing pieces of christianity were philosophical, and that alone tends to explain one part of what was and wasn't sucked up in the resultant vacuum.
The other part is that the Jesus movement was very much "thinking on its feet" during its development. There was a lot about the life of Jesus that didn't ressonate with the standard narrative of the kings of jews of yore (for a starter, he died an apparently ignoble death and didn't capitulate the roman overlords), so tweaking certain dates to passover helped implement a certain strategy. There is a lot of questions on how Jesus viewed himself, whether hd really did see himself as a political reformer of Jews, and how political events in post-Herod, post-client king Jerusalem ended up determining a major course for events.
Jesus didn't really turn up on the Roman radar until he started drawing uncomfortable gatherings in the newly designated roman province state, which seasoned the atmosphere with ideas that had obvious connections to Judaic themes of Jewish people throwing off the shackles of their oppressors under the guidance of a divine king. There is a question on whether this path of political appeal to Judaic revisionism was part of the "mission" of Jesus, or simply something he was thrust in to by others, which led to a substantial anticlimax when events took an apparent reversal.
And then you see the jesus movement fall upon hard times as they exclusively seek membership amongst (reformed) jews. Despite a tangible status appeal (in certain regions during the state of the the Roman disintegration) of being Jewish, there were various deterrents to converting to Judaism (least of all, getting circumcised in adulthood). Hence there was an audible sigh of relief amongst vast numbers of the adult male population by the time Paul got his gig happening. So there is a point where the early christians scratch their heads and ask themselves why they are beating their heads against a brick wall by trying to only draw membership from Jews. So there you have a second sort of vacuum, determined by bridging the cultural gap between Jews and non-Jews .... which, again, hardly sees an opportunity to throw down ancient Egypt as a major playing card.
All in all, I'm inclined to think that the Trinity was the product of early Christianity's attempt to hang onto three items of doctrine that they felt were essential to Christianity. The first was the single monotheistic God of later Hebrew scripture. The second was the divinity of Christ, whose incarnation and resurrection were the basis of Christianity. And the third was the Holy Spirit, which popular Christian belief held was active among the people.
Jesus came and exclusively described himself as the son of God and gave a few teachings in this regard. A few hundred years later there were a range of things being taught in the name of christianity that had no connection to things being spoken by Jesus. For a long time, describing Jesus according to how Jesus described himself was grounds for being killed. An important aspect of the holy ghost is that it provided scope for legitimizing a bunch of doctrines brought forth by various institutions/persons. This gets into interesting territory when you start to examine the historiography of biblical passages that go at lengths to reference the holy ghost.
So there was obviously a problem avoiding the charge of polytheism, which groups like the Jews leveled at the new Christians. (And as Islam was later to do.) The challenge was how to hang onto all of these three things, how to continue thinking of all three as divine, while retaining the belief in only one God.
IMHO, the detractors of the trinity introduced the charge of polytheism because its easier to strawman your opponent on a slippery slope ("Oh look! Three gods! Before you know it they will have four or a dozen!"). Perhaps it may have been different if there was no hushed or overt accusations of polytheism to dog the proclamation of the trinity doctrine, but there was never any serious spill over in to polytheistic expression in christianity. I guess you could problematize that claim on the strength of conservative islam, but then you wojld be stuck to define such a claim as the moderate ground (as opposed to existing as an extreme within the category) for defining monotheism.
What's more, the whole thing took place in the shadow of the Christological controversies, in which Christ's nature and his relationship to God were hashed out. Trinitarian theology and Christology needed to be consistent, which greatly narrowed the space in which they could maneuver.
Given that there was an already established preponderance of thought over two things, the son and the father, one has to wonder whether moving on to three things is not just the logical consequence of having unsatisfactory categories as time and tide brings forth new demands.