We had an issue like that, same kind of thing, with a surgery where they sent something to a nonparticipating lab. What helped was that for an identical surgery (left and right side kind of thing) a month earlier, they didn't do that, so we had a good argument to make that it was their fault for choosing an out-of-network lab.
They eventually agreed and covered it, but I *think* they would have had to anyway, since the hospital itself was in-network. My wife spent probably 10-15 hours over a couple of months making phone calls, reading things, sending documentation, etc. to get it sorted out. She does a lot of that and is very good at it, so she knows how to interpret the paperwork and charge codes on things. It is definitely annoying that today you have to be your own doctor, lawyer and accountant just to be sure other people are doing their jobs correctly, though.
Definitely have your coworker appeal, read the details of their insurance coverage (not just the 1-page summary HR gives you), and keep following up. Ask to speak to higher-ups, emphasize that the facility was in-network, no notice of out-of-network use was provided, etc. Worst case it should be possible to get them to knock the bill down to what the insurance company would actually pay, which is usually 10-30% of what is actually billed these days. Even if they spend 20 hours at it, that is still pretty good compensation per hour.