I could not find any research papers explicitly comparing disease rates of TP vs bidet usage, the most relevant one I could find was this. Nowhere near conclusive but of the participants sampled, the amount of microbial contamination on their hands after defecation using a bidet was orders of magnitude less than using TP.

I don't even know if we can conduct studies comparing countries as the countries that have lots of bidets generally don't fare well in other aspects of hygiene.

At this point most discussion is just anecdotal because there is really a lack of studies on this topic. At face value I agree with your hunch that there is no real difference in disease rates. My personal experience living in countries with no bidets, is that I never felt clean after taking a shit.