craftsman drill press run out

How does the chuck mount, is it Morse taper? If they loosen and spin the bore and shaft will be damaged and THAT can cause runout.
yes, it just gets tapped into place

it was on there firm when i got it
i did see a little bur on the taper that i filed down, but that didnt seem to help

i think i will take it all apart and see if i cant find a wobble in the spindle itself