Did you receive a Reservation of Rights letter from your insurance company? What paper correspondence have you received to date?
Also to add - I spent some time talking to some current property adjusters and we are all kind of in the same boat. To begin with, the wording choice of the first person you spoke to is fairly important. "That should be covered" isn't a commitment of payment, especially if they add something to the effect of "your adjuster will make the final decision." So in this first step, it seems like it would be a you vs. them argument.
The next part is fairly immaterial. "Hey we use servpro and they do good work." That isn't anything but a recommendation based on their prior experiences. So ignore that.
This next step is a contentious issue. If the insurance company said "yes go ahead and do the work, this is a covered claim" to servpro then the insurance company is responsible for all work done up until the day of denial. If it was just a confirmation that there is in fact an open claim, then there is no coverage promise. Should be covered is not in fact covered, and interpreting that statement incorrectly doesn't afford you coverage.
There is a general concept here called detrimental reliance which is more of a contract law term but applies. First and foremost, there must be a promise. In this case, it's a statement that says "this is a covered loss" either verbally or written, and a reasonable person would interpret as such. Without that, you don't really have a leg to stand on. BUT, the insurance company may still pay a portion or the full amount of the work up to the date of the denial statement. Since homeowners is first party, some companies are favorable to mistaken communication. I have paid for things just because I knew that someone heard me wrong or didn't actually understand the intent of an endorsement when they had it added, never the full amount but enough to say "yes I get that you weren't listening and I'm doing you a favor here."
And just as a point because you mentioned it - homeowners insurance pays for sudden and accidental. That is the core driving concept of property and casualty insurance. All endorsements and exclusions are written in a way to pay for "OH SHIT" and expressly not pay for "fuck it I'll deal with that later."