re: How to handle bill from AC service company if nothing was fixed?

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the problem may be bigger, and likely more expensive.

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This.

The guys who came out likely thought that what they found needed to be fixed, fixed it, turned it on, it worked, and that was that. There's nothing dishonest about this but it does mean the real problem might get missed.

If you want someone to take the extra step of looking for more stuff that wasn't immediately obvious, that will cost extra. And then you will complain about why you paid $400 for someone who did take that extra step but found nothing when some other company did it half-assed, got lucky, and only charged $200.