By any reasonable definition, Ukraine is in Eastern Europe, whether you use geographical, political or historical definitions. This is what Wikipedia says, as do most atlases and the CIA world factbook, in fact I've yet to see a source saying otherwise, but you can surely provide links to one. The EU is not the same as Europe, by that narrow definition, Switzerland is not Europe. Your statement that nobody in/from Europe or Ukraine would say it's in Europe can be disproved with a simple counterexample: I'm from/in Europe and I say so, just as a random sample of my Ukrainian acquaintances.
No comment on Russia being "by no means" European. I guess you'll need to do a lot of Wikipedia editing to remove all references to Tolstoy from the pages on European literature.
In my experience it's only people from the US and possible the UK and/or Scandinavia that only think "Western Europe" when they say "Europe".
However I would say this type of shorthand is far more widespread than UK and Scandinavia. My German friends adds Eastern Europe when speaking of Ukraine, too, as does my Italian friends.
The cultural differences in Europe are far more complex than an East-West divide. Saying that Ukraine has a European culture is like saying India and Japan have "Asian" cultures. It sure doesn't make them the same and frankly, it does not even very similar.
Google (or books) are your friend :)