I would say it is less precise because it gets fewer string cross-sections
That doesn't exactly explain a lot.
"Precise" in what way? More precisely righteous? More precisely bassitudinous? More precisely orange with a tint of green?
If you're thinking that it should be more precise because it picks up a shorter length of string, I'd be interested in why you would think that the P would be less precise than a Jazz, which (I feel silly pointing this out, but given the original question, I'm not taking any chances) has TWO pickups, and therefore picks up string vibration at widely separated locations.
As noted, the Precision was named that because it was considered an improvement on the "imprecise" standup bass, which had no frets and therefore was subject to poor intonation in the wrong hands. The P was
so precise that even a g**tarist could play it in tune. Don Randall, who formed Fender Sales with Leo Fender and others, and who was responsible for the "Broadcaster," "Telecaster," and, yes, "Jazzmaster" names, said that Fender himself insisted on calling the bass the Precision.
I have a fretless Precision that I made up a decal for that says "Fender Imprecision" but I've never installed it.