I would assume they probably use tor or residential proxies in order to get around any ip related rate limiting
And yes, Kopeechka controls the inbox, and only lets you see stuff going forward that matches the regex you specify.
Tor traffic meets the rest of the internet via exit nodes. There are a finite number of exit nodes and some sites seem to know what they are at a given time and may block the traffic or present a bunch of extra captchas.
Ask anyone who uses Tor for their day-to-day web browsing. They're often given additional CAPTCHAs and the like. Some sites block them entirely.
Tor might hide where you're coming from, but to any website, it's obvious you're connecting from Tor.