Those definitely look like water spots to me. @oldturkey03 has a lot more experience with this than me, but my guess, assuming the spots aren't on the surface, is that there's a good chance you could disassemble the screen and clean the individual layers of polarizer, LCD and backlight. You just have to be very careful to reassemble everything in the exact same sequence and orientation you took it apart in, and of course whatever you do, don't apply too much pressure to the LCD; if you crack it, it's pretty much game over.