I know because I'm snoopy (or curious)! I also became independent in 2004 (effectively starting my own agency) so I really need to know.
The IRS rules are solid, it is just the agency perspective versus the traveler/taxpayer perspective that doesn't align. Tax home status has so many variables that it would be impossible for any agency to really get it right every time. Hence the level of due diligence that they do do. And the advice to learn about it yourself or get yourself an expert like TravelTax.
I don't know about Fastaff's regular assignments, but for staffing strikes, hotel rooms are the norm and they are shared. They also specialized in rapid response assignments. Those pay more for good reason, for whatever reason, those are usually troubled hospitals. Sometimes they are post strike, sometimes they are inner city hospitals with a sketchy patient population and staff willing to work there, sometimes they have the state regulatory boards coming down on them heavy so they need to beef up unsafe staffing levels. Regardless, few hospitals pays those kind of rates unless they have to, otherwise they would just get regular agencies and rates. But Fastaff does pay well, and usually working 48 hour weeks (their norm) plus extra hours on top of that can get you over 200K a year if you can handle the hours. Personally, I travel to travel and you can't absorb much of the area working that hard.
For ordinary travel, you should aim for $35 hourly including per diems as good pay (plus housing on top of that). Or $50 as PanTravelers calculator figures it is excellent pay. If you are getting five bucks less, that is OK too. This is highly variable though based on location, specialty, and hospital needs.