I can point to a conversation on these forums where a woman stated she had pity sex with guys, for pretty much the reasons I laid out - that's what pity sex -is-, it's having sex with someone out of that sense of obligation arising from a perceived social advantage. It's not like I took an entirely fictitious example and presented it as an analogue of real-world things, they're all real-world things, and they're not the only ones.
You're stating that they're different, but that's from an objective outside perspective; from the inside obligation feels like obligation, regardless of its reasonableness.
It depends on who exactly the person feeling the obligation is. For example, I definitely don't feel obligated to write Web pages for free for anyone who asks regardless of how busy I am.
P/S/A: There are single sentences which can create life-changing amounts of difference.