Wait -- why would canned (i.e., "preserved") tomatoes be not from scratch? Do jam thumbprint cookies not count as "from scratch" if you don't make the jam yourself? How about balsamic vinegar -- do I need a vat of wine to let ferment for a dozen years in my basement? Man, the list is endless -- dried spices and fruit, pre-shelled nuts, pretty much every condiment ever invented, any kind of oil or butter or cheese or sausage, etc.
Even the Italians use canned tomatoes for pasta sauces, because really good tomatoes captured right at the peak of flavor and preserved are far better than the middling stuff that comes out of the local grocery store in February (or even September).* I figure if it's good enough for the Italians, it's good enough for me.
My definition is pretty much like
@MyAlterEgoIsTaller -- if it's a basic ingredient/staple that can be used in a bunch of different ways, then it's cooking from scratch, even if someone else preserved it or created it for me first. That includes some multi-ingredient things (I'm sure as hell not going to make my own Worcestershire sauce or fish sauce!) and, yes, tomato paste. Even though someone else did some of the work for me to get it in that state.
*I also know some Italians who grow their own tomatoes and then go into a frenzy of canning/preserving when they ripen so they have their own home-canned tomatoes all winter. But not everyone can own a farm, ya know?