If you're providing a service to your users, and they say that the service is down using pingdom, you should be looking into, not just saying "Works on my machine".
I mean, what qualifies as “being up”? If some random link in the middle of the Internet goes down, and you suddenly, for 30 seconds, are unreachable for the few hundred people going through that exact link because it happens to be the best path between those people and your server, can they claim that you have failed to provide adequate uptime? If such a fault happens, are you then responsible to troubleshoot it? I say no. The Internet is the ISP’s responsibility, and the only faults actually meaningful to report to your ISP are the repeatable or long-lasting ones. Small stuff like this is not worth anybody’s time (except ISPs) to go digging into.
You've seem to think that you have to investigate the issues. On the contrary, you bump it up to your isp to investigate. If your ISP is regularly having these issues then it might be time to change ISPs to one with a better peering agreement.
1. Reported as being experienced by an actual user of a web site,
2. Longer than a a couple of minutes at most (usually just a few seconds),
3. or happened more frequently than a few times per month,
then I might consider reporting it to my ISP. As it is, it’s not worth it. “Cosmic rays, man.” (https://www.joelonsoftware.com/2001/07/31/hard-assed-bug-fix...).
If Pingdom can't get to your site, it's highly likely your users can't either.
Multiple ping locations is helpful in bringing more data points, but it doesn't address the problem of explaining what the data means. For example, pingdom could provide triangulation of the failure if fault identification was part of the businesses model of monitoring.
I would describe the criticism of pingdom as a failure of expectations. Pingdom is not a security service, a monitoring service, or fault identification service. They are a single test, and the data you get back is useless unless interpreted and verified.