If they had removed the belt, they would have found that the bearings were going bad. However, that's not a common thing to check unless it was making noise. If it went this soon after buying it, I would be surprised if it was quiet. How stable was the temperature gauge since you bought it? Did it ever overheat before? The bearings went away and while it may be repairable, it may be better to just replace it.
Don't run it until the pump is replaced. That's your raw water pump, by the way. You have aluminum heads and they really don't do well with overheating. Also, if you ever need to replace the circulating pump, you can't just go to an auto parts store and say "I need a water pump for a Chevy 350". Yours is Corvette-specific and cools the heads before the rest of the engine. It's called reverse cooling and it's not the same part. The raw water pump you need is slightly different, too and it's in the link below.
I don't know if you'll be doing the work on your motor but if you will and know about this motor, great but if you don't, you may want to get a manual. The side panels come out and this makes working on the motor a lot easier. The sun pad has a pin that hold it onto the ram and it's a waste of time to try working on anything under it with the deck in place, but you DO NOT want to just let the deck flop back because it'll damage the gelcoat, fiberglass and the deck. I used a piece of rope with a snap hook on one end and a loop that would go over the ball on the pylon. I would let the deck open about 30 degrees past vertical and it makes life a lot easier.
The alternator needs to be loosened, then rotated down so the belt and bracket can be removed. There's a small machine screws (Allen head) on the bottom of the pump that will need to be removed, then three or four larger machine screws hold the pump onto the crank pulley. Pull the hoses and make sure they go back on the same way they came off- the lower one is the supply and the upper one feeds the thermostat housing. Don't go Ape squat when you torque the bolts on- they all have lock washers, so 25 ft-lb should be fine on the larger ones and snug will work on the lower one..