Typically, when you have a battery that's a few years old, it's a good idea to replace it when you're replacing the alternator. That 5 year warranty doesn't factor in a failing alternator, and an alternator that's going bad can 'go bad' over an extended period of time (days or weeks) - causing repeated deep cycling of the battery which reduces the lifetime of the battery.
If your alternator failed suddenly and quickly, you battery is likely fine. If the alternator failed slowly, your battery could be closer to the end of its life than you think. This is an extreme anecdote (as in, it likely won't happen to most people), but years ago we had a car with a dead alternator and an older battery - naturally, we swapped the alternator and kept the older but still barely warranted battery. About a day later, the new alternator bit the dust - the old battery was so depleted that the new alternator burned itself out trying to keep the electrical system operational.
Now that it's getting cold, I'd keep an extra eye on the battery, especially how long it takes to turn the car over in the morning. If it's struggling, it would be good to swap the battery. I think the parts store was probably trying to sell you a battery that you may not have needed, but they had a just cause to recommend the swap.
Oh, and when you send the core back, they're not looking for the same brand of part, they're looking for the part that would have been installed on the car be it OEM or aftermarket.
