There are more polite and productive ways of asking for proof of the phenomenon. Or, better yet, use Google the way it was meant to be used, and find out for yourself (just search for stories about DNS migration/propagation issues). People have documented visits to their old IP addresses for a very long time (much longer than the TTL) after updating their DNS with new IP addresses.
I don't see how you could construe my comment as being in anyway impolite.
Google does not turn up any useful results for this subject. The only reference I've seen to resolvers doing something unusual with caching is on the dns-operations mailing list where I ran into a fellow who doesn't cache records with a TTL less than a minute.
Since you claim it is simple to find a resolver that extends the TTL beyond what the authoritative server has specified, can you please point me to such a resolver?
EDIT: Just to be clear, I'm after a server that I can query or something equally authoritative.
EDIT2: My apologies if this is seen as belaboring but please note that nicksuan's comment is not referring to CPE, stub resolvers or client apps.
Your original comment is impolite because it is presented as a demand without any explanation. A demand of proof without explanation can be interpreted as an accusation of lying. Something like, "I haven't seen this phenomenon myself; could you link to some example bad ISPs or articles documenting it?" would be much better.
As for proof, I'm not a professional sysadmin, but based on my reading the most proof you're likely to get is indirect proof in the form of requests to IP addresses long after they've been removed from DNS. If those requests are concentrated in a few ISP subnets, it's reasonable to infer that it's the ISP, not customer equipment, that is caching beyond TTL.
Your interpretation of my original comment seems extremely hypersensitive to me. Perhaps there is cultural difference at play here.
The experience I've had in hosting ten-thousand odd zones suggests that these resolvers do not exist. I've seen a great many claims but am yet to actually see a resolver that extends TTLs in the wild and so I consider them all but myth.
In the past there has been issues at the client - predominately with browsers, MTAs and stub-resolvers - so if I were to observe activity that suggested a stale cache I'd be more likely to attribute it to a bug (be it new or old) if no other data were available.
