This error reoccurred, this time not involving older Macintoshes, but up-to-date patched, clean, unmodified Windows with Internet Explorer 11:
Turn on TLS 1.0, TLS 1.1, and TLS 1.2 in Advanced settings and try connecting to
https://bitcointalk.org again. If this error persists, contact your site administrator.
All those protocols were already enabled, and this time I'm positive that my ISPs (plural ISPs) were all working correctly and there wasn't man-in-the-middle or any other shenanigans going on.
The time stamp are in the range:
2015-07-23T00:00 UTC
to
2015-07-23T00:31 UTC
and this time I ran several tests on various ISPs and various OS installations.