That is a brunt valve, and I had no doubt they'd send you a picture of one. As I intimated, I'd have higher level of confidence if you'd seen in person through scope. Did the say which valve exhaust or intake valve?
Good read on possible cause
@AimCOtaco. To take it a bit further as too why; Bad oil due to lack of regular oil changes (poor maintenance) damaging valve guides or plugged injector from using cheap gas. I'd like to see oil pressure readings, to get read on bearings before head swap just in case oil related issue. If you can verify regular oil changes and oil pressures is to factory spec, then a head swap may make senses.
@Grass, Compression needs to be done with engine at operating temperature, all plugs removed, good battery (I use 100 amp changer/starter attached to battery) fully charged, throttle plate open (I forget too often), pull EFI fuse (don't want fuel pumping), then crank 5 times minimum. I just watch gauge for highest reading then stop cranking. Check all cylinders to see balance (difference) between them.
By pressurize cylinders (somewhat of a Leak test) you can confirm Shop's picture and which valve they say is burnt: Intake (air sound coming from throttle body) or Exhaust valve (air sound coming through exhaust pipe.
Just a thought to save a buck; You don't actually need a leak down tester. Pick the correct compression gauge kit that has a quick connect setup, that will fit your (assuming you have) air compressor quick connect. Some adapting MAY BE REQUIRIED. You'll need the hose with thread fitting intact (and tight) to set down into spark plug tube and thread in. Then pressurize cylinder on compression stroke either before or at top dead center.
Note: You can turn crank bolt buy simply remove skid plate to access harmonic balancer to crank bolt.