I know what Slash has said about Izzy's playing after he left, that it was much more tight and heavy with Gilby. And I know that there are some credit mistakes, Izzy doesn't play leadguitar on DTJ and doesn't play guitar on Coma and Locomotive (his parts weren't agressive enough), but I've never read anything about Don't Cry... and I've read lots of interviews
I'm pretty sure Izzy does play on Don't Cry, it sounds like him.