RE: need some advice from moms of mellow/reserved toddlers...
My DD (2.5 y.o.)is exactly like your DS. Once one of the kids from playgroup had her hands around DD's neck (like she was strangling her) but DD didn't protest - so I thought the other girl may not have used too much force. I sort of stepped in and said be gentle or something (the mom didn't). DD told me much later that she got hurt. I was so upset that hadn't stepped in earlier.
I have started teaching her to say firmly, 'Don't do that. It hurts me.' when kids push her or get physical otherwise. She does say it sometimes but the other kids don't always listen. But atleast she's making a stand. Often her saying that will cause the other kid's mom to step in.
Also, like a PP said accidentally pushing is different from deliberate things like strangling (yep, I'm still bitter about that)!
If your friend wants to teach her DD about sharing/taking turns, that's great and I would be fine with that. Her DD has to deal with other kids too, whose moms may not be so understanding as you. Your friend doesn't need to apologize to you each time though :) so maybe you can tell her that.
Also I've sort of resigned myself to the fact that my kid is never going to be the aggressive, fight-for-the-toy kind and that's fine. It takes all kinds to make the world :)
“Live a good life. If there are gods and they are just, then they will not care how devout you have been, but will welcome you based on the virtues you have lived by. If there are gods, but unjust, then you should not want to worship them. If there are no gods, then you will be gone, but will have lived a noble life that will live on in the memories of your loved ones.”
― Marcus Aurelius