The probability calculations involved in producing those rules would be based on the stated criterion as is.
That is the calculations that led to deciding on 9 in the rule "nine points in a row on the same side of the mean" would be based not on how far they were on that side, just on them being on that side at all.
So - as arbitrary as it may seem - if you want the rules to retain their supposed properties (both the false alarm rate and the chances of detecting something when it's actually happening), you would use them as stated. If you want to vary the criterion, you would also vary the number of points so that they retained the properties they were designed to have (or to deal with the consequences of changing those properties).
If you modify it so that you need 9 points beyond some point further beyond the mean, you'd reduce the false alarm rate and the power to detect problems at the same time; that's not automatically a problem but (i) it would be best to be very aware of exactly how much you're impacting both those things, and (ii) people aware of Nelson's rules might look askance at the modification without a good justification for it.