It is an extremely counterintuitive result, I agree.
The basics are that your standard grocery store plastic bag is made of a very very small amount of plastic, and thus a very very small amount of oil went into it. The environmental costs of travel were amortized across many many more of them because they travel in these massive multi-packs to be used in bulk, and so forth. I am not sure how disposal enters into the mix, precisely... I’d think the comparison is “here is how much crude oil is needed to make the gas you need to chainsaw down a tree to make a paper bag and ship it to the store, versus how much crude oil is needed to make and ship the plastic one.” That is, the assumption is that they both get sent to the same landfill, compressed into a small little cube, and shuffled off to some corner similarly... No thoughts about plastic bags blowing in the breeze.
In a related note, when I was a kid I remember being shown, as we passed, some recycling center... And I remember being scandalized about the dark smoke being belched out into the air. I am told that they have made great gains since I saw that, so that glass and metal recycling is now fairly clean, but that plastic recycling is still somewhat dicey in whether the recycling process yields a net environmental benefit. I have no idea if that's accurate though, it's a very faint memory.