I don't think that claim is accurate at all! Bifidobacterium are also anaerobic bacteria, and they're present in almost all probiotics.
I found this paper which covers the topic of oxygen tolerance in probiotic bacteria. (http://www.horizonpress.com/backlist/ciim/v/v5/01.pdf) From what I can tell, the encapsulation used in Prescript-Assist would limit the exposure to oxygen.
It's actually a good question you asked, but the answer is not as simple as you might think. As long as the exposure to oxygen is kept minimal, the anaerobic bacteria should survive. As to how successful Prescript-Assist is in doing this, I can't answer that question.
But the fact remains that something in it has a profound positive effect on my condition. I reasoned that it was the Bacteroides because of its role in the GI tract, but it could be one of the other 28 strains included. But really the only other strain that's native to the gut is Pseudomonas. The other strains are soil-based.