Of course you can throw one source of propaganda at another source any time so don't waste your's or my time, but do you agree that Obama's administration first introduced a relaxing of attitude towards Assad well before the Trump administration came into office or not?When you have quite different memories about the wishes of the US. The main military point which motivated Putin was that the turkish-backed took Idlib, which made the whole situation dangerous. The US were wishing nothing of this at all. But they were unable to say so openly, given that Putin was invited by Assad to fight islamist terrorists, including Daesh, and to support Daesh in a completely open way was impossible for the US.
Nonsense. Putin has clearly and openly declared from the start that it will fight all terrorists, and not only Daesh. This was at a time when, even if officially Al Qaida was on a list of terrorists, there was no US fighting against Al Qaida at all, and almost open support of various "moderate rebels", which were, in reality, factions of the same Al Qaida renamed into FSA or so.
There was an initial big propaganda campaign "Russia is not fighting Daesh, as they have claimed", but the natural answer was that, first, there was no such claim to fight only Daesh, and, second, they were fighting Daesh too. In fact, the first big success of the Syrian army after the Russians came was the breaking of the siege of the Kuweiris airbase, which was against Daesh. Another anti-Daesh action which became quite famous was bombing their oil business. Daesh was not the priority - initially, the priority was Latakia, because of its potential danger for the coastal area, but also because of a large amount of fighters from Caucasus there. After this, Aleppo became priority. Clearing the rural area in East Aleppo from Daesh was part of it, but of course not the main part, which was Aleppo itself. Clearing the environment of Damaskus is high priority, and will remain so for some time until the job is finished. Actually fighting Daesh is sufficiently high on the priority list. But if there are some attacks from Idlib, then to stop and revert them has clearly much higher priority. Roughly, Russia has his own priority list in Syria, and it is based on its own interests, and has never made any different claims. The US position in the UN was irrelevant.
Putin was hesitant in getting involved in Syria with the USA being so severe in it's attitude towards regime change. However when the USA Obama Foreign Affairs team** suggested that the USA priority was shifting towards the defeat of Daesh, Putin had an opt in, which he took advantage of. ( that degrading Daesh was a higher priority than regime change)
**I can not recall whether it was Kerry or the UN ambassador or other.