This levelling business set me wondering as well. I can think of a few reasons for doing it. One is that it puts the machine in exactly the same orientation as when it was originally ground, so you should be replicating the original accuracy. But I can't believe that you need a precision level to achieve that - I'm sure that you could get close enough with any decent level. But a precision level might be able to check for twist by checking in various places along the bed and save time spent in machining a test bar until you were very close. If you also set the machine very accurately, you could also use the level for setting work later? I've never done that, but I can see it might be useful on a milling machine.
By the way, don't use the tailstock for setting up. The initial setting up is all about getting the headstock aligned to the bed (or vice versa). That's why you don't use the tailstock when doing the initial checks. The tailstock is usually adjustable, and has to be aligned with the headstock and bed later. I wouldn't trust tailstock alignment on a fresh-from-the-factory machine.