I'm with you on not knowing the actual math behind it. My anectodatal evidence is that the most I've EVER had on credit cards around statement time was ~$3000, but at the time my available credit was around 100,000 (it's about $110,000 now). Edit- by $3000, I mean $3000 that I paid off after my statement generated - I've never paid interest.
My credit score during that time frame was ALWAYS between 780-800 at 2% utilization max. It's now between 760-780 for the most part. It took a nosedive AFTER I paid off my student loans; they like you to have mutliple TYPES of credit too, and now that credit cards are all I have I lost some points, though it seems to be trending upward (all time low that I've ever seen was 760 on the nose).
So I'm fairly sure that with zero debt and minimal credit utilization, you can still have an optimal credit score for mortgage rates (the only debt I consider OK, personally).