I'm not sure my lathe could do better than a thou on an 8" facing operation, but then it's not adjustable.
It might be a bit less than a thou in 8", and a bit more in 12". Facing flat verifies that the headstock is parallel to the motion of the cutter on the cross slide.
For the rest:
Here's the thing: a twist in the bed creates exactly the same effect as a tailstock that is not centered on its adjustment pins. It moves the tailstock center laterally with respect to the spindle center. When you have two adjustments that might create the same effect, you have to isolate them to check them. That's why I start with pinching a razor blade between centers, with the quill retracted nearly all the way. That puts the tailstock as close as possible to the headstock, which minimizes (but maybe does not eliminate) the effect of any twist in the bed. Once the tailstock is adjusted using that test, you can be more confident that the tailstock is centered on its adjustment pins as well as possible for the moment.
(If you attempt a two-collar test without centering the tailstock first using the razor-blade test, you won't know whether the tailstock is uncentered, the bed twisted, or both. And there is even the possibility that for the specific length of your test bar they are both wrong but offset each other leading you to believe that everything is aligned.)
Then, back the tailstock away from the headstock and do the two-collar test. If it's cutting taper (the two collars are different, or the measurement of a two-collar measuring device such as the one from Edge Technologies using a dial indicator on the carriage is different), then it's less likely to be caused by tailstock adjustment and more likely to be caused by bed twist. If the tail end collar you just skimmed is smaller than the collar at the head end, then the tailstock center is rotating away from you as it follows the twist in the bed--shim the back right corner up a bit. If the tail collar is larger than the head collar, then it's rotating towards you as it moves down the bed--shim the front right corner up a bit. Once both are the same, go back and pinch that razor blade again. If the blade still stands at right angles to the spindle when it's pinched between centers, then your tailstock is centered and the bed is flat with respect to tailstock and carriage motion, or at least as well as one can do given the wear on the bed. You might have to back and forth a couple of time.
A tailstock can also be turned a bit on the bed if the v-groove is worn crooked. (This is in yaw, while a bed twist affects roll, if those aviation terms mean anything to you.) Ask me how I know! The only cure for that is scraping it in, or finding a better tailstock. I tried the latter and got lucky. If it's turned, the tailstock center will shift laterally as the quill is extended, which is not good.
A test bar with a morse taper on one end, inserted into the tailstock and run up to a center in the headstock, can expose a range of maladjustments, as long as the test bar is really accurate. I have one of those Indian test bars, but I'm not sure I really trust it. I'm more comfortable trusting the Edge Technologies alignment bar, or just making my own two-collar bar.
You can also measure bed flatness using something like a Kingway, but that's really for measuring it when scraping it in, and it still needs to be twist-free before attempting that.
Did that explain my reasoning? Is that what Rollie's dad also suggested? (I found it easier to just explain what I do and why than try to find faults in someone else's approach--who may be starting from a different point or with a different set of assumptions.)
Rick "been through this several times with a 76-year-old lathe that has been reground at least once in its long life" Denney