Cordelli has replied while I've been looking up links...

In the very early days, the US said "3 ounces" and the rest of the world said "100 ml" which of course are different. Within a few days or weeks, the TSA changed their rule to "3.4 oz" which is (nearly) 100 ml, and officially that's what you're allowed. However, the signs had been printed and the PA announcements recorded to say "3 ounces." Over at the PV (the TSA blog) and here on FT, many people asked why the signs and announcements couldn't be updated, and the consistent answer from TSA (as formalised in this link given by Cordelli) was "it's too hard, it's too expensive, and besides, you all know we really mean 3.4." (Note that the distinction between fluid ounces and ounces avoirdupois was also too hard, so they ignored it.)

One TSA person who posted here tried to argue that the "real" rule was 3 ounces but they had latitude to allow you up to 3.4 ounces. No, I never believed that either.

Officially the rule in the US is 3.4 ounces and it's on their website here. There have, however, been reports of individual screeners who claimed that the rule was 3 ounces, and who confiscated unilaterally allowed the passenger to voluntarily surrender a 3.2 or 3.3 ounce liquid. There was even one story of a screener who claimed that a container labeled 3.0 ounces was not allowed because "3.0 is more than just 3" Or this thread, where a 0.25 ounce bottle was confiscated because the screener thought it was 25 ounces.

As with everything else to do with the TSA, if you run into a screener who claims that 3 is the limit and tries to confiscate a 3.2 ounce container, you can try to show them a printout of the website but you'll likely be told that it's out of date or "we don't do it that way here" or "anyone could edit a website printout."

So, tragically, "the TSA can't do math" is one of the genuine answers.