On two occasions I have "re-interviewed" current or past developers who wanted to move up from working on extremely simple low-complexity code / sysadmin work, and start working on our flagship project. In both cases the team leads and I didn't think these people were qualified to do so, but the candidates were really convinced they were. These were employees who had come into the company through non-standard channels, so hadn't experienced our normal interviews.

I had them attempt to solve the problems on a whiteboard that I would give to our intern candidates. Both totally bombed hard, and our other "re-interviewers" had the same result when they asked some design-related and algorithmic related questions.

This wasn't "regurgitating algorithms". It was basic problem-solving and software design. From their track record of development we didn't believe them to be qualified (despite their own opinion of themselves), and they only confirmed it by totally bombing the "re-interview" process (which was identical to our normal interview process).