I'm a little surprised they quoted you $310 for a logic board to be honest. Is this Apple Depot place an authorized repair shop and are they giving you a brand new logic board ordered from Apple? Apple charges more for logic boards, I think.
A few things...
$310 is a discounted "flat rate" cost for out of warranty repairs. They do this specifically to provide reasonable rates to owners of out of warranty Macs that are suddenly faced with otherwise high repair costs.
The problem with this though is that Apple has to warranty any repair they do either for 90 days or the remainder of AppleCare, whichever is longer. This means they have to return the Mac to you in a warrantable condition, i.e. a condition that is free from dents or other damage. While I agree the dent is likely unrelated to the logic board failure in Apple's eyes they have to replace that top case (which IS accidental damage thanks to the dent) in order to provide warranty on the repair, otherwise both Apple and the owner face a problem should the Mac's hard drive (or other component in the trackpad area) fail within that 90 day window. If they don't replace the top case, and the hard drive fails two weeks after the Mac is returned, then they are in a situation where the damage could have very well caused premature failure. It's not Apple trying to screw people, obviously because $610 is still a good price for a MLB and top case with labor involved, it's Apple trying to keep a consistent and fair repair service.
Apple's depots are definitely authorized. They are essentially large warehouses filled with ACMT technicians who repair Macs all day long, 6-7 days a week. The parts they use are the same parts that Apple would toss into a machine if it was repaired in house at an Apple retail store or an AASP. They may be brand new (if the Mac is new enough) or more than likely refurbished and heavily tested, same as any other manufacturer out there only with likely higher quality control.
My advice to the OP - Call AppleCare / Apple Customer Relations and explain the situation. If the Genius who checked in it made note of the dent at the time of quoting the repair then point this out to whoever you speak with. The depot is almost always much more scrutinizing when looking at any sort of damage but it's not uncommon to see AppleCare push a repair through regardless of the depot's findings. Hopefully they take care of you! Worst case you might have it returned (should be no associated costs), remove the battery/hard drive and attempt to fix or lessen the dent, then send it back in. You could also check top case replacement costs through an AASP as that + the flat rate repair might still be cheaper than $610.
Good luck!
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Did just that and got a call from executive level support. They're repairing it for the original $310 fee!
Awesome! Ignore the end of my last post!
(That'll teach me to reply without reading through the entire thread!)