The phrase would just as soon means the user would prefer one option to another. It is a comparative phrase that sometimes leaves off the second half of the comparison.
The confusion comes when the phrase is heard instead of read. If the speaker’s annunciation isn’t clear, as soon can be interpreted assume. In some cases, assume can make sense in the sentence (e.g., I’d just assume it was done.), but the actual phrase is as soon.
I’d just as soon been forced to go see the musical “Oklahoma” — which, come to think of it, I wasforced to go to as a kid — than suffer the indignation of being pinched on the cheek and told how cute I was. [The Albany Herald]
The fact that we regard many of these places as our territory, and we’d just as soon keep it smelling of nothing much, doesn’t seem to occur to them. [The Guardian]
But maybe after he wrote 100 of them and watched them get buried by a Facebook algorithm, or observed how people just look at a silly number on Rotten Tomatoes to make their decisions about what movies to see, he’d just as soon as throw in the towel and become a bus driver (not that there’s anything wrong with driving a bus; maybe it’s even more helpful than reviewing movies). [Huffington Post]
They’d just as soon see new power plants, and jobs that come with them, be constructed in Ohio or Indiana. [The Detroit News]