[nitrogen]

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.

[frooby]

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.