You've heard correctly; coconut is not botanically related to tree nuts (it's actually a drupe).  For some reason, a few years ago the FDA decided to declare coconut a tree nut and require labeling for it like tree nuts even though it really isn't. 

The only reasons you should avoid coconut is if you are allergic to it (which would be unrelated to any tree nut allergy) or if it has been contaminated with tree nuts at the manufacturer.

I've ready so many different things about where coconut falls as far as allergy concerns.  Most have said that coconut is in a different family than tree nuts, so it is safe to eat.  But I've noticed alot of packaging says "May contain tree nuts (coconut)".  It has been years since I've had it, so I'm nervous to try it as I've developed new allergies after testing.  What has your experience been like?  Is coconut safe to try?  Is it in any way related to my other fruit allergens? (kiwi, plum, melons)