Nope. the tension would be the same when the string is in tune. His problem is that the length of the string is under the right tension, but the note is only right when open. The length of vibrating string when fretted is actually slightly too long, causing it to go flat. The further up the neck, the more out of tune it becomes.
Shorten the length of vibrating string, and not only will his open string needto be under less tension to be in tune, but all the tuning issues will be gone
