Congrats on your two medals, Jeff.
No doubt the brewer's skill, choices of ingredients and water profiles, and attention to sanitation also played a role. 
Was the use of medical O2 the only thing different between this year's success and previous years?
There are so many things involved. That is why I said would those have placed without? Who knows.
You want to optimize everything you can for competitions. Anything to give the yeast a happy environment really helps.
For many beers you could make a great beer without O2. One of the best Ordinary Bitters that I have ever made was with shaking, then a "double drop" at 16 hours or so to introduce some more air for the yeast. Been thinking about dooing that again.