Thanks! After so much of research, I found that 'noindex' in a robots.txt is not a directive. But still I am very much confused since the 'robots.txt checkers' available online do not find the use of 'noindex' as an error and report to us, why is that?
And also whey you say "I say specifically google, because That Other Search Engine has indexed a few pages that are clearly and explicitly labeled noindex"
Do you refer to the NOINDEX in robots.txt or NOINDEX in Meta Tags?