It is not the STM of the lens itself that is the limitation. In video mode, the DSLR uses live view which means it must use sensor based focusing for autofocus. The 600D and older Canons (including the 60D) only have contrast detect autofocus in live view which, while more accurate, is also very slow and leads to very obvious 'hunting' for focus. The 650D and later models have a hybrid on-sensor autofocus that brings phase-detect to live view which is much quicker. It is with this autofocus mechanism that the STM lens becomes important – because previously, due to the hunting issue, videographers avoided autofocussing in video and therefore the sound, as well as jerky transition, was not much of an issue.
The 650D features version I of the hybrid autofocus and the 100D and 700D feature version II of the hybrid autofocus. The 70D takes this idea to a whole new level with dual-pixel autofocus.
Whoever told your dad that the only difference between 600D and 700D is a touch screen is extremely ignorant. There are several differences which makes the 700D a much more advanced camera:
* Digic 5 processor vs. Digic 4 on the 600D; gives better low light performance and higher burst rate (5 vs. 3.7 FPS)
* All 9 autofocus points (in viewfinder mode) are cross type, vs. only centre autofocus point being cross type in the 600D
* Stereo microphone
You can find an exhaustive comparison of 600D vs. 700D in DP Review's 700D review.
Again, all these differences matter only if your kind of photography needs these additional features. The 600D with a twins lens bundle is available at a very nice price now and presents excellent value for money, leaving more funds for all the other stuff you will need for your DSLR, like a good flash, tripod, etc.