If you move your blog to a subdomain, you shouldn't, by any means, keep it in the folder due to duplicate content problems. You can only move it, not copy it.
About your question, for my experience it's not true and you should keep your blog where it is right now.
This happens because the main domain has the main strength and power and dividing it to subdomains will only dilute this position. Subdmomains are great for separate panels, logins, user areas where you'll want, for example to have separate access control.
I did some research and found a reply from Rand Fishkin from moz.com that backs up my position:
I would still strongly urge folks to keep all content on a single
subdomain. We recently were able to test this using a subdomain on Moz
itself (when moving our beginner's guide to SEO from guides.moz.com to
the current URL http://moz.com/beginners-guide-to-seo). The results
were astounding - rankings rose dramatically across the board for
every keyword we tracked to the pages.
I've had the opportunity to see many dozens of other sites do the
same, almost always with similarly positive results (assuming they're
moving from a subdomain without much other content/link signals to the
subdomain that has those signals).
Taken from here.
Here is also a greate resource from Moz about domains.