Sorry for the late reply!
I tend to use my Live Plus mostly these days and finally got around to swapping the Live back in to test.
As far as I know, the latest official firmware has no issues with YouTube.
My Live is running the latest Beta (1.03.38) and that certainly has no issues with YouTube (just tested it out!).
Not 100% sure but I think firmwares prior to the latest official firmware didn't respect YouTube's No Syndication flag, so content that wasn't permitted on TV enabled devices would still display, and YouTube eventually blocked Live units with older firmwares. That may have caused some rumours that YouTube wasn't working.
Also, the No Syndication option is used quite frequently now, resulting in a frustrating amount of content that won't play. Doesn't make it any less annoying but that's a YouTube limitation, not specific to WD players.