Alt volts

Had some trouble today. Car wouldn't start, so got a jump. Got a new battery (was a really old battery anyway, so figured it was time). When I got home, I decided to grab my multimeter and check things. With the car on, I've got only 12 volts on the new battery. Decided to check the alternator and I've got 20volts!

Checked the voltage regulator and it's within its usual range. I'm thinking the alternator must have gone bad and is overcharging, and that it most likely blew the fusible link, which is what caused the dead battery to begin with.

This sound right?