I recently was reading an article on how to ring a pig. Applying hog rings to the snout of a pig is to prevent rooting behavior. By the way, I don't ring my pigs. I've read articles on the internet of how short nosed breeds of pigs don't have a rooting behavior, but I don't think that's accurate. All pigs root up the ground to some degree or another. Some people say the certain breeds don't root, while others say just the opposite of the very same breed of pig. Personally my experience says it depends upon the individual pig. Some definitely like to root more so than others.
All my pigs so far have been mixed feral types. Some have more domestic pig in them than others, but they all have been at least 50% feral. Some of them were avid rooters, others had little interest in rooting other than scuffing the surface.
My current pigs, Lava and Shelly, aren't big rooters. Yes they root a bit, but their hearts aren't into it. They snuffle here and there, but generally grass grows just about everywhere in their enclosure. They have one spot that they like to churn up rocks, but that's it.
I often see recommendations on various farming/gardening forums to use pigs to "plow" the garden. I don't see that as great advice for a few of reasons. First, not all pigs are avid rooters. So you can't just order "2 piglets please that will be good rooters". Second, they are selective rooters. They surely aren't going to go down your rows and politely plow up your garden beds. (You will notice in the photo that my pigs haven't rooted most of their enclosure. The grass is doing just fine!) Third, some pigs just snuffle the surface, while others like digging down to China. So instead of plowing, they are more apt to make lunar landscape craters with deep foxholes here and there. You will end up with more of a headache than when you started. Top that off with the fact that pig activity tends to leave behind compacted soil, I personally don't see the benefit of using pigs to prepare a garden site.
Bottom line........if you want your garden tilled, I wouldn't rely upon a pig to get the job done. Use a rototiller, plow, or shovel instead.