The hottest temperature for the least time always gives you best results.
It is difficult to imagine where or how this instruction arose. Just as “low and slow” is not always the answer, so this also has its application, but not as a general practice.
In general, I try to get my fusing work done in 10 minutes at the working temperature. Any less time there and I feel I am trying to go too fast.
Advancing very fast normally requires a higher temperature than a slow advance, to get the same result. Also with a higher temperature you do not need to have as long a soak as at a lower temperature.
It is more difficult to get repeatable results with fast firings. A more controlled rate of advance will allow the controller to cope with any variations (e.g., power, or mass of material being fired) present.
But you need to know why you are doing the AFAP for as short a time as possible. It can be useful for small and jewellery scale items. It certainly is not applicable to larger or thicker items.
For slumping, it may be that the reverse of the headline suggestion could be the appropriate response. Slow advances allow the glass to gently conform to the mould without excessive stretching. This is also helped by using a low temperature and a long soak.
These observations show that the injunction may be appropriate for some work, but most kiln work is better done with a slower, lower, longer approach. This means slower rates of advance, lower target temperatures, longer soaks.