Not knowing you or your family, I couldn't say which one of you remembers it accurately. I know some people just have poisonous families and a lot of lies and mis-remembering of shared pasts does happen. Then again, depression affects your mind pretty heavilly while you're dealing with it, so it is possible that you don't remember things accurately yourself.

Honestly, I think you may be the only one can decide which scenario is true. If your family has supported you in the past and you are in a good place now, it may be best to just let it slide and let them believe they supported you, whether that is the case or not, so that you can move on and get on with enjoying your life.
That said, if you find your family tending to claim to be supportive after the fact without having actually done so, especially if it happens on a regular basis, you may want to look at moving out and getting distance from them for a while, to clear the air if nothing else.