This sounds like fraud to me. Fight it legally!
A co-worker told me that this happened to her, and that made me not take the in-network only plan, but I got the PPO instead. I still think it's illegal or morally not right what they are doing, so we should all fight this practice!!!
Sadly this is how hospital stays are conventionally billed. The cost of being admitted covers only the bed and routine nursing, literally everything else is billed separately. As unfair as it is, the best patients can do is vehemently question the necessity of any interaction with a physician, or else get billed for it. And good luck with that if your case is complicated and you're getting referrals to a wide range of specialists.
And honestly, when you're admitted to the hospital unexpectedly, you're probably not in the frame of mind to be questioning everyone who comes by. I know when I was in for a few days, I only recognized the name of one of the hospitalist doctors that later billed me. And the bills can come months later!