Stockpots in the oven
I would think that there is no reason that a stockpot without plastic trim/parts should not be oven safe.
That said, a thin walled stock pot is not really going to be the right choice to braise/roast in the oven with radiant heat. Nor is there any benefit to cooking stock in the oven...
I guess it depends. I use a Dutch oven for a stock pot. Perhaps her mom did too and thinks it's a stock pot.
I think I'd get her one of those. It's extremely versitile. Pasta, soup, stock, stew, no knead bread beans, greens, I could go on and on. In the oven, on the cook top and slow cook.
I'd guess she means a dutch oven. there's really no reason to put a stockpot in the oven; good size ones would be too big anyway and aren't really designed for in-oven use. Cast iron are good for this purpose, as they retain heat well and the heavy lid seals in lots of flavor. you can get either a round one or an oval. It would probably be too small to serve as a stockpot though.
The pot in the oven makes sense for two reasons:
1) Roasting the bones: Fill the pot 2/3 full with bones and vegs for roasting.
2) Simmering evenly: Add water to the top of the bones, lower the temp to 250F, cover, and the simmering stock will extract flavor over several hours.
The stock will come out rich and gelled.
Having heat penetrate gently from all sides seems to help, rather than bottom only.