Wow, that's a weird one!
This is clearly a bug at archive.org — I can reproduce it by manually sending HTTP requests to their servers, without involving SE in any way. What appears to trigger it is the combination of:
using a short archive URL of the form
http://web.archive.org/..., as opposed to the longer form
having the browser send a HTTP
Referer (sic) header with a URL whose path portion begins with some letters, a slash, some numbers and another slash (optionally followed by more text).
It just happens that SE question page URLs like
http://meta.stackexchange.com/questions/286411/... happen to match that pattern, and so will trigger the bug, but a referrer URL like
http://example.com/a/1/b will trigger it just as well. For example, here's the output of a quick command-line test using lwp-request:
$ GET -USed -H Referer:http://example.com/a/1/b http://web.archive.org/http://foo.bar/test
User-Agent: lwp-request/6.03 libwww-perl/6.05
Date: Mon, 31 Oct 2016 01:18:29 GMT
Client-Date: Mon, 31 Oct 2016 01:18:29 GMT
Set-Cookie: wayback_server=12; Domain=archive.org; Path=/; Expires=Wed, 30-Nov-16 01:18:29 GMT;
Also, note that these responses are cached pretty aggressively by the archive.org servers, so sending a second request for the same URL with a different
Referer header will still return the original response (with
X-Page-Cache: HIT instead of
MISS in the response headers).
The reason this doesn't (normally) happen with
https: links is because, for security reasons, most browsers won't send cross-protocol referrer information. So if a plain
http: page links to an
https: URL, no
Referer header will be sent. Of course, if you happened to be reading SE over HTTPS (which mostly works), you'd see the same bug with
https: links too.
Fortunately, while this is really a bug on archive.org's side, the workaround is pretty simple: always include the
/web/* part in archive.org URLs.
Of course, the SE automatic URL detector won't handle URLs containing an asterisk correctly, so you'll have to use the Markdown
[link text](URL) syntax. But that's a good habit to get into anyway.