The preferred shop takes a haircut on the job because that is the basis of their contract with the Insur. Co. So essentially costs are fixed so either they take a hit, they pass part of it on to you by taking a few short cuts or they just do an really BS job and you take the complete hit; looks nice, but underneath who knows except for the actual guy that did it and being an employee he will have his own set of standards depending on his relationship with his employer.
One thing is for certain; few ppl take them to to task after the fact because it simply isn't in most ppl's nature to really push things because it's exhausting.
So do you have leverage

Well the Adjuster will say that the body shop ppl are fully responsible for all errors for the "lifetime" of you're ownership experience so you're all good as if that really changes anything. Consequently, the body shop is on the hook for this extra cost. Do they in turn, make the employee(s) who worked on the car fix it unpaid (call back) ?
It sucks, because under the preferred cost arrangement there is no allowance for errors which are statistically going to happen.
If it were me I would not mention calling the adjuster to the shop manager. You need to go for a ride with the shop's representative and nail it down. Get his observations written down on a work order and you getting a copy of those "findings". It won't be pleasant because if they actually record the problem then they own the issue. You don't want, and I'm sure this has crossed your mind, something to the effect; "leave it with us and we'll have somebody look at". You need an official admission that it's still not fixed as original.
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Ultimately, you can call the adjuster and say you are writing the President of the company, naming the Adjuster, and taking your business elsewhere. That's the final step. There is no "Insurance Referee" or practical legal action available.
Hang in, you never know.