Well I finally had some spare time last night and I took the chuck apart and tried just the back plate, cold not see any wobble whatsoever. Same when I reattached the body, no wobble on the front face of the chuck that I could see. Then I tried with the jaws, but I used the 2nd set I had and the rod I spun in that wobbled a lot less than it had before. More than I'd like, but less, so perhaps it's the jaws, I need to put the other set of jaws on and repeat the test.
Not wrong, but there's merely no guarantee it'll run true on another machine. If build quality is good & consistent, there's no reason it shouldn't though.
You could check for run-out of either backplate or chuck without a DTI. Mount solidly a piece of metal (preferably) with a domed end close to the back-plate/chuck in the position you need to check and use feeler gauges to measure at 90* degree intervals of rotation, By hand of course,
Indeed. Its hard to see how it would run true straight off on another machine without slackening the mounting bolts and bumping it. The probability of two machines being so identical that you'd just see the chuck run out alone would be pretty small I would have thought.