Gosh, in my experience doing agency only occasionally, it definitely depends on the facility. Had to refuse one assignment--it was a 30-bed vent unit, and I'd never done vents, and wasn't about to learn that way.
In another place, I wasn't told that I was "the" RN for the building, and in the middle of report a CNA ran up to the desk yelling "Fire!" The
staff LPN giving me report looked at me and said, "Oh my gawd, what do we do?" -- I sorta felt compelled to take over there; no time to refuse.
And in yet another facility, I followed another agency nurse who apparently had worked a few shifts there, and was not real popular with the staff. She informed me that she'd just DC'd a Foley on a new admit at 11pm, while I was in report. I wanted to make sure the pt. was voiding before I started my 6 am med pass, and went in to check on her. Guess what? wrong patient's Foley was DC'd. The staff nurses were ready to hang the agency nurse until I discovered, waaaaaay back in the beginning of the month, an order to DC that same Foley. Ergo, agency nurse unwittingly corrected a staff nurse's mistake. DC'd Foley on
right patient, thencalled the Doc on the other to see if maybe he wanted Foley reinserted (pt. heavy, fragile skin, hemaplegic, on Lasix, and requesting to keep it), but even half-asleep, he was adamant--leave it out. To make matters worse, after I dealt with all that and got my 6 am meds out on time, the staff nurse screwed up report completely and reported me to my agency as the nurse who DC'd the wrong Foley instead of the one who discovered both mistakes and fixed 'em. I was kind enough to go back the next day and explain the whole thing to medical records. But if I hadn't caught the staff nurses' mistake, they'd have hung that other nurse out to dry.

No, thanks, I don't wanna work there ever again....