That fuzziness is probably the default behavior.
In Radio Config > Channels > Channel 0 (LongFast, probably) there's options for position enabled which will report a general area within a radius(?) of the slider a bit further below. There's also a toggle for precise location which does what it says on the tin. But everyone with the same radio settings and channel 0 settings (likely almost every other meshtastic node in the area) will also receive your precise location, as I understand it.
I was just explaining the cause of the fuzzy position, but sounds like you've already got your head wrapped around that.
Agreed, I imagine most people (myself included) don't want their exact location sent over a public channel.