I mean, even if it did imply that, so what?
If "B will be awarded a new series and will next snap the ball" = go on the snap
..then if B is "awarded" a new series and is not next to snap the ball, go on the ready.
I don't mean to disparage my fellow officials, but there have been a few times in recent years where there was a discussion about a rule that seemed to be clearly written and unambiguous resulted in a long discussion from somebody who just didn't get it. One that sticks out to me in particular is invoking the numbering exception for scrimmage kicks and there's a long discussion of what "between the ends" means.
To that end, I'm a little leery of rules that are written to be unnecessarily complex. I feel the editorial committee likes to pretend they're lawyers and writing legalese to sound smart sometimes, and it's just... well, you've read the rule book. I don't want to risk unintended consequences because we're writing rules to try to cover every possible scenario, just to invent a few more that nobody ever thought of.
For example, and this is just a devil's advocate situation, somebody reads that rule that R receives the punt on 4th and 15 and is tackled in bounds at the K5 after a long return, therefore the result of the play is R being awarded a new series. However, R had a 12th man running off the field at the snap, and K accepts the 5 yard penalty from the previous spot -- but since we awarded a new series to R, then gave the ball back to K, somebody interprets that as an A-B-A scenario and it's 1st and 10 for K. That is, of course, very wrong, but I fear putting the idea of "R can be awarded a new series, but doesn't keep the ball" in somebody's head.
To that end, I'd be a little more concerned about that official wanting to enforce that foul as PSK or (worse) from the succeeding spot.