Brit here. I have heard this in advertising over here too. I think it’s more a case of ad execs thinking this formulation is somehow more psychologically effective. My guess is that saying ‘all x *are not *the same’ is somehow deemed to sound like a stronger refutation of the imagined claim that ‘all x the are the same’. I definitely remember a major ad campaign where the tagine was ‘because all (?) are not the same’ but I can’t for the life of me remember what the product was. I just remember finding it slightly jarring.
For my money this nails it.
Maybe it’s my mathematical mind, but I totally agree with the OP. I grew up on the US and have lived well over half my life in Canada, so I don’t think it is British v. North American.
FWIW, I traced “All that glitters is not gold” back to the original Latin which clearly said “Not all that glitters is gold”. As far as I am concerned out current aphorism is claiming, among other things that gold does not glitter. It makes no sense.
Going back to the OP …
I agree that US usage is typically like “all cars are not blue” really means “some cars are blue, and some are not”.
Said another way “all cars are not blue” should be interpreted as “not(all cars are blue)” rather than as “all cars are not(blue)”. The negation is lifted from the adjacent adjective to apply to the whole phrase. Which can be ambiguous in complex sentences where you can’t unambiguously determine how far up to lift the negation.
I’m no Brit. But in the British writing I read they’re usually careful to put the “not” at the place in the sentence where it negates only what immediately follows it.
I’m not sure how much this is truly a matter of Brit versus US as opposed to sloppy & colloquial versus precise & learned.
In my experience most speakers in the US say “not all cars are blue.” The phrase “All cars are not blue.” Would be used in a specific context for emphasis to counter a specific statement or implied statement. You’d more likely here it to counter a prejudicial statement; e.g., “All Muslims are not terrorists.”
It seems to me like “all x are not y” is another instance of scope ambiguity. The scope of the negation could range over the predicate, or the whole construction (negation excluded). Compare modal ambiguity, e.g. “if phi, then you should psi”, where the scope of “should” could range over psi, or the whole construction (should excluded).
Sometimes it might mean that, but surely “all x are not y”, for an American, could have the not range over just y. For example, “all cars are not bikes”, I’d guess, would have a narrow scope for both Americans and British.
If true, I don’t think this means that the British can’t hear “all x are not y” with a wide scope. For example, “all planets are not the earth”, or “all planets are not in the solar system”, I’d guess, would have wide scope for both British and Americans. I could be wrong.
**American logic and grammar **
That’s like a double oxymoron.
But not very like one.
You could try this one out on
All American logic and grammar is not like a double oxymoron. : )
I’m a Brit. 
I personally would write:
“not all cars are blue” = some cars are not blue
“no cars are blue” = there are no blue cars
I don’t care for the construction “All (something) are not (something)”.
I agree with the OP. You hear “all are not going on the trip” when they mean some are, some aren’t. This is illogical - not all are going is correct. The not needs to go with what it refers to.
Not all anecdotes are evidence. Or all anecdotes are not evidence. Whichever you prefer.
IMHO, this would be a GQ if it were likely that someone provided a citation to an actual scholarly linguistic study of the provenance and prevalence of the two phrasal forms.
A more on-topic IMHO: the American form is superior because it attaches the negation in proximity to the negated, which is consistent with other modifier-modified relations in English.
Once again we see the failure of the language to properly use parentheses and other symbols to clarify a statement. I would prefer to write !(all cars are blue).
I agree with Colibri on this one. I’m an American. And the normal way I’ve encountered is “not all blanks are blank”.
The alternative of “all blanks are not blank” is far less common. In fact, I’d speculate that when somebody uses that unusual construction, they’re trying to sound erudite like Tolkien or Shakespeare.
In other words, when an American says “all blanks are not blank” they’re imitating the way a Briton said it.
I’m a Briton who has lived in the US for the last 19 years. You’ll have to decide the sound mind bit for yourself. But to me, the construction that begins with “all…” is archaic (which likely explains why the printed examples raised in the thread are all fairly old.)
I haven’t noticed people saying the thing which this thread is about.
Where it could possibly happen is if someone get tied in a grammatical knot. It could happen if a person makes a assertion like “all cars are blue” and it’s countered with “they are not all blue” repeating “all cars” instead of “they.” There would have to be an “all ___” being talked about first.