I could've written your post about my dd actually, in fact I think I wrote a very similar post around 6 months ago when dd was about 2.5. We'd go to a toddler group twice a week, both quite different, one more physical and bustling, the other library-based. She prefered the latter but at both she consistently clung round my legs and would have a couple of bouts of tears. She never once, seriously once, wandered off into the room without me. I tried loads of different tactics. So i was dreading her starting at a playgroup this September (I did start a thread about that!). On the first morning I stayed and even though I told her I wouldn't play with her there she barely left my side and cried a few times. I think the staff were looking a bit dubious . Next day i told her I was going to leave her, gently reminded her a few times that there were no other mummies there etc. etc. etc. and I dropped her off, she gave me a 'brave' kiss with slightly quavering lip. And ... and ... she didn't cry once all the time. She played with the toys and did the activities, asked the teachers for a wee and didn't ask for me once. When I picked her up I saw her skipping down a corridor holding another girls hand!
So ... my conclusion is that a lot of this stuff is done in relation to their relationship to us as their mums. They might even somewhere think we 'expect' it of them. It's too complex to speculate what goes on in a toddler's mind. But honestly if you'd seen my dd in a toddler group you'd never have believed how she settled into playgroup. Without me there.