As you know, there has to be compression but there's also playing with a compressed hot sound (Arturo, MF, Doc) and not compressed (Balsom doing Bach).
One of the things that may have been omitted is the vowels:
Generally when people use the Tongue Arch, they are told to also think of shaping the tongue, "aaaaaaa"
as in "apple" for the low register and "EEEEE" for the upper register. The sound "aaaaa" is created by having the tongue on the bottom of the mouth and the chin is generally dropped a little whereas "EEEE" is created by moving the tongue closer to the roof of the mouth which usually causes the chin to raise. It appears that people that use the tongue arch and/or vowel sounds incorporate the chin so that may be the reason the tongue arch works to make playing more effective/efficient in the upper register. It appears that more than just the corners make the aperture smaller for people that use this method.
So where does this leave us?
It appears that "faster air" or "compressed air" and other similar terms (one of my favorites being how Bud Brisbois described it) are used so we can actually understand what it should feel like when we incorporate these methods. The underlying mechanics appears to be when the tongue is raised to say "EEEE", the chin also raises which helps make the aperture smaller.