Trouble is, with Welsh you can't be completely sure. There certainly was a Gaulish equivalent of "Theodoric", which was "Teutorix" and meant exactly the same thing (Ruler of the People).
All the Brythonic peoples looted Classical Antiquity and recent (to them) history quite heavily for names for their children. Sometimes the borrowings are obvious, sometimes less so. And when you have two names as similar as "Theodoric" and "Theodore", and the former name has fallen out of use for centuries - some people will go for what seems obvious on the face of it rather than digging any deeper.
I also wouldn't put it past old Owen to be using both meanings simultaneously: a "Gift of God" who would be "Ruler of the People".
Must admit I knew of Theodoric "The Great" for years, but Theodoric I was a very recent discovery - and there's a bit of a surprise lurking in the "Legacy" field.... http://en.wikipedia.org/wiki/Theodoric_I