My experience is that when a company is big enough to have a legal department, they invent a bunch of terrible scenarios and then create policies to protect the company from the things they imagined. Yes, there can be real problems hiring contractors directly (but I think it's fairly rare), and it's a lot easier to have one or two agencies that you pay instead of dozens (up to thousands like the company I'm working for now) of separate contractors.
Billing the big corps (when it's possible to contract corp-to-corp) has been a pretty awful experience too. Adobe wanted to see my company's client list, tax returns, and marketing materials AFTER the work had been done, for an invoice under $20k. I said no, and it took over 2 months to get them to pay. That was a while back though, so maybe things have changed.