NO online presence (online profiles) = NO short-listing for a job interview. Is this true OR is it a myth?

Absolutely myth because alternatively we can complete the CV screening and shortlisting.

I'm of the opinion that it is absolutely crucial for an individual to haven an online presence in today's world while applying for a job. In regards to short listing though, there are a few things that need to be taken into consideration such as - Position applied for, Company Policy, Fresher/Experienced Candidate, Location they are applying for (Local, National, International), etc. It may not be a rule of thumb and while many recruiters may not even look for an online presence of the candidate, but with the technology at our disposal it's imperative that you have at least a professional profile on a site such as LinkedIn.