It seems that Saudi Arabia or Bahrain’s regimes tend not to get called 'illegitimate', so 'not democratic' would not imply 'illegitimate'.

I think it’s more like this: Governments the US doesn’t like very much are 'illegitimate' because 'not liberal democracies'; regimes the US does like are 'important allies' or otherwise not talked about.

The whole 'not democratic' thing is more like a type of post-hoc justification for what, to many, looks like blatant imperialism. It would appear it is successful at least some of the time.