Clip, clip clip ... is everybody happy?

Agreed. Thicker air equals lower speed. FAA equals even lower
speed.

Not necessarily - thicker air also = much more thrust. It's all pretty
much a wash, with a transonic airplane. Usually the TAS in units/time
(mph, kts, km/hr) is higher, but the Mach Number's a bit lower. *The
Speed of Sound is proportional to absolute temperature. It's warmer
near the surface, so there's more mph/Mach Number.

Generally not true. Indicated airspeed top end is usually highest at
low
altitude, but true airspeed capability will rise with increased
altitude.
This all assumes no airframe structural limit, which is frequently below
the
aircraft's capabilities in commercial designs.

John, I have to respectfully disagree. While I don't have the
specifics for a 757 or 767, here's a list of the thrust/drag limits
(Which often exceed the published flight limits) for a number of
similarly performing transonic military aircraft. The data sources
are teh Standard Aircraft Characteristics for each aircraft, which
uses the same flight test data used to create the Pilot's Handbooks
and NATOPS.
All are Standard Day conditions

Sea Level 35,000' Notes
Vmax Vmax Mmax Vmax Vmax Mmax (Placard Limits, etc.)
KTAS KEAS KTAS KEAS
F-86H 600 600 0.91 545 304 0.94
B-47E 545 545 0.83 485 270 0.85 Lim. 425 KEAS/M 0.86
B-57B 521 521 0.79 475 262 0.83 Lim. 500 KEAS/M 0.83
A-3A 545 545 0.83 510 284 0.89
AV-8B 575 575 0.87 528 294 0.92
S-3A 430 430 0.65 443 324 0.72 Vmax is at 20,000'

Of all the examples, the S-3 comes eth closest to, say, an airliner,
with its fat body and high bypass engines. Even so, there isn't much
difference. The thing driving drag the most is Mach Number. (The drag
rise due to compressibility getting going) Since Mach 1 is about 85
Kts lower at 35,000' than it is at Sea Level, It's not too surprising
that you'll have more knots in hand at low altitudes.

The problem with your comparison is that it shows only SL and 35K
(tropopause) speeds. An examination of PsubS curves would show zero PsubS
increases slightly with altitude to a point (well below tropopause) and then
suffers the mach effect as you describe giving slightly slower speeds in the
stratosphere. The issue is engine efficiency versus transonic drag effects
and normally produces results as the S-3 illustrates. While most of my high
speed experience (approaching placard etc) is in supersonic aircraft
(different rules, different PsubS curves), I recall the A-4 exhibited a
similar behavior ... faster at mid altitudes than either very low or very
high.

I'd like to know who the brave soul was that pushed a B-47 120 knots over
its airframe limit ... funny structural things happen in such cases.

R / John