That's one way to say
Einstein was wrong I suppose.
It sure is. And what's empirical, is that there isn't any time flowing through a clock. A clock features some kind of regular cyclical motion which is counted / accumulated and displayed as "the time". So what else is empirical is this: when the clock goes slower when it's lower it's because that motion goes slower. Even when it's a light clock. You will of course be familiar with the parallel-mirror light clock. It's an idealised clock, but nevertheless it's used extensively in relativity. For example, in the
simple inference of time dilation due to relative velocity. That's SR time dilation. For GR time dilation, you arrange one parallel-mirror light clock above the other like so:
View attachment 161
See how the lower clock goes slower? It can only do that if the light goes slower. Of course you'll find a way to dismiss that too. And it will probably involve some abuse.