I also did some searching but couldn't find any other evidence that 1.7.2 does not have demo mode (all results for "minecraft 1.7.2 demo mode" turned up people who were stuck in demo or the like); according to the Wiki only versions older than 1.3 do not support demo mode (prior to then a special standalone version was used) and will let you play without restrictions:
If one tries to play a demo version prior to 1.3 from the launcher using a non-premium account, they can play the full version. This is because 1.3 is the version that added the demo mode to Minecraft, so earlier versions do not have the code necessary to recognize that they are in the demo.
Granted, the results that I found were all quite old (from the time 1.7.2 was the current version), maybe somebody else can verify whether 1.7.2 still runs in demo mode. I did note this following entry in the history section of the link above:
1.7.2 Users can no longer play the demo mode in minecraft.net.
However, this has to refer to the removal of the original online Classic version, which was restored in a slightly different form last year, and has nothing to do with 1.7.2 itself..
I noticed long ago that 1.7.2 works without demo mode.
One day I was just playing old demos for fun, and I discovered 1.7.2 but I thought it was by design, although I was always wondering why.
Version 1.7.2 is fully launched not only from the author of the theme but also from me. Screenshots for proof. I even manage to play on servers.
My Mojang account was registered a long time ago, but I never bought the game. I have no idea why this is happening.