I would still be very careful of processed foods, especially the salt content. It does depend on what your LO is having throughout the day, not just at one meal, so it *might* be possible to have a taste of something you are having which you wouldn’t ordinarily give him. For instance when we went out to a restaurant I would make sure that DS didn't have salt in anything else at all that day so he could have a small portion of food whilst we were out, I wouldn't have done that every day though.
I always gave DS what I was eating but changed my cooking so that foods were zero or low salt and I knew how much of a portion would be ok. (for instance regular shop bought bread is high in salt in the UK so I worked out a half slice per day was the max DS could have with say a tablespoon of canned beans in sauce - a meal I would very rarely give but did once in a while).
You could make spaghetti sauces and pizza in a healthy low salt way for the whole family rather than using processed foods. A plain pizza base or something like a flat bread with tom puree, cheese, and various toppings for instance would be fine for LO where as a shop-bought pizza may be more processed and higher salt than what you could make at home with store cupboard ingredients.
There's quite a different between a 10 month and 13 month old so although I don't feel there is anything wrong with pizza or pasta sauce (just a small portion occasionally if processed, more often if home made and healthier) I also wouldn't be too influenced by what another parent is feeding their child. A 13 month old has double the salt allowance of a 10 month old, which is quite significant.
hth