The position held by other photographers wasn't "you couldn't do anything else with our time".
That was precisely the position held by some photographers, notably the one who basically accused me of being an unethical person just for examining the idea and asking questions. If he pays someone to cover an event for three hours, that person had better not take other pictures during those hours. It's "double dipping" (ugh!), and he'll be "blackballed" (eek!). Don't you remember? (Granted, I have more reason to remember, given that I was the one attacked. I tend to remember such incidents.)
I was talking about a possible situation in which you're at an event and someone other than your client asks you for photos, which may be additional ones besides what your original assignment calls for. I'm bringing up this past discussion because that situation is similar to what the OP described, and no one so far has mentioned that agreeing on the spot to take shots for someone attending an event is frowned on by some hired photographers and those who hire them.