Read some oil analysis stuff. The cheap, recycled bulk crap that you get in a $20-30 oil change is indeed breaking down by like 2000 miles.
Maybe at Jiffy Lube, but I don't think most dealers do that.
All of the Honda dealerships over here use Honda's synthetic blend (ConocoPhilips) in their $29.99 oil changes. Ford dealerships use Motorcraft synthetic blend (also ConocoPhilips). Both are very good oils.
That said, my mechanic lets me bring my own oil + filter, so I bring what I want to use and pay him to do the oil change and also do a basic inspection, tire rotation, and top off other fluids.
The cost ends up being just a few bucks more compared to what the dealership would charge, but at the end of the day, I think it's well worth it to have an ASE master technician do the work compared to a lube tech getting paid $8 an hour at the dealership. I saw him do the oil change one time and he actually spent a solid 10 minutes checking the dipstick 5-6 times as he filled it up to make sure it was spot-on. I'm pretty sure most dealerships just dump in 5 quarts and call it a day.