I would start by calling the hospital and asking about the charge first, since they seem to be the ones who charged it, unless I am misreading it. I would also see what the insurance company has to say, as well as touch base with the doctor's office billing to see if they know anything about it, but I think your best info will come from the hospital itself.
We had it happen last year when DH was in the hospital. Turns out the extra billing was for a "consult". Things can get so confusing in a hospital (and I work in one) so it wouldn't surprise me if someone from the primary care group actually did consult but word never got back to the primary care physician. Do you know if the hospital and the doctor's office use software that "communicate" with eachother? Some systems don't, so they rely, still, on things like faxed information and that sort of thing, which can fall through the cracks. These are the things I'd be looking for.
I've also posted before that in the past several years I've had to sort through numerous issues like this - when you get multiple separate bills for hospital stays. (We had a $35 bill for an EKG after DH's stay, as well, which seems absolutely crazy since he had multiple EKGs during his stay and we were only "charged" for one! My guess is that somehow the person doing the EKG didn't "transmit" the information electronically properly and it somehow didn't get to the right place for billing. But I digress...)
The latest fiasco I had to deal with - since this past September - was finally resolved in our favor. But it took months, and I actually got a call from a collection agency while this was going on, which infuriated me since I'd been working on it and supposedly it'd all been resolved. But what happened was DD had to see a consulting doctor, separate from the surgeon, before a surgery she had scheduled. We were approved for that visit from our PCP's office. Well something came up and we had to change the consult appointment time, and the only time they had available was with a different doctor in the same group, so we took it, not realizing, or being informed from anyone, that it would apparently require a whole new authorization. So since we hadn't gotten a second authorization, we were charged almost $1000 for the visit. Each of the parties involved - the hospital, the insurance company, and the PCP's office all had a different take on it. It was super frustrating having to go back and forth repeatedly with all of them, making sure things were done, and done correctly.
We basically resolved it by the PCP's office confirming that the visit was authorized, and they were able to provide the original authorization number from June (which I know doesn't make complete sense, ie why didn't it work for both doctors then if it did now, who knows) to both the hospital and the insurance company by faxing it over to them. (Ha! The FAX issue again! Turns out the insurance company will only accept info by FAX if you can believe that. This receiving dept will also NOT take phone calls from customers, only from doctor's offices or hospitals. I spent an inordinate amount of time trying to get someone on the phone, but ultimately I was only able to "speak" to a general customer service rep!

) Anyway, somehow, the hospital followed through with contacting the insurance company confirming the authorization, and the insurance company received the authorization also, but - and here's the zinger, and what caused them to put is in collections - they don't automatically re-submit authorization corrections!

So although they had it, technically, it wasn't "re-submitted". So it took numerous phone calls AGAIN after I got the calls from collections to straighten it all out once and for all. Sorry so long, but just trying to illustrate how nuts these things can get, and how frustrating it can be trying to resolve them. The lady in the hospital billing dept assured me she'd call me if there were problems, and she never did, so I *think* on their side they also thought things were all set. The biggest problem was the insurance company.
I will say from being a long term hospital employee from the days when most things were on paper, to now, where much is electronic, it's been a cluster, in large part because some of the systems don't "talk" to eachother yet, and this creates a lot of problems. I think things are headed in that direction, but not everyone's there yet. We once had a presentation from the head of my hospital's computer systems and it was really interesting what he had to say about this. New systems had to be incorporated into old ones - without their ever shutting down (and thereby disrupting hospital operations; unable to do for even a day. Lots easier to put in a new system than to try to add to old ones, often multiple old ones in many cases). Even though we've made progress, there's still a lot of older systems out there trying to combine with newer ones.