Couldn't find the original study,sounds like an interesting read, could you possibly link it?
Sounds believable that 13 gallons is optimal, but then again, 1000 gallons is probably optimal for a Oscar, doesn't mean one can't live fine in a 150. That's just my reasoning on it. Not advocating for undersized tanks by any means. Just think that "optimal" is not always possible/necessary.
But I did find a PDF by Maryville College, and they tested 2.5 gal and 5 gal on tanks both with and without heaters.
It was found that 2.5 gallons was not acceptable for Bettas, being to small