Rear brake caliper sticking

I run out to do a quick errand and on my drive back to the house I smell the brakes burning. (5 miles) When I get to the house I verify its the right rear. I jack it up and sure enough it doesn't budge. So I give the local dealer a call to use my extended warranty as I have 40 k on my 2009 and he tells me that caliper is covered but pads/rotors are not. He hasn't seen my vehicle but is already telling me I need pads and rotors (which I swapped at 27k). Left side is wearing evenly but right side innermost pad is about 1 to 2 mm thinner. I just priced calipers at $45. I feel like buying the caliper and slapping it on for less than my deductible, just concerned dealer will flag my car. I also need a 5yr drivetrain inspection. Any thoughts cause I smell a $500 bill, I am amazed that a pads/rotors aren't covered on a caliper failure.

Thanks