I do some research on evolution as part of my day job, teach about antimicrobial resistance as part of that job (e.g. I understand evolution quite well), and I have to say that I was deeply unimpressed by the podcast. Resistance to a treatment - man-made or otherwise - is inevitable. Proper use of the treatment methods (which, IMO, is a huge issue in beekeeping that is also poorly researched) can delay the evolution of resistance. But even with optimal use, resistance will eventually arise. That's the nature of evolution.
The problem with the claims in the podcast is that they ignored the fact that chemical resistance is not the only resistance that can evolve, and that resistance to bees natural/evolved anti-varroa mechanisms will also occur - and is equally inevitable. And delaying the evolution of varroa to bee's intrinsic resistance mechanisms is far more difficult, and will fail far faster, than delaying resistance to chemical treatments. The reason for this is two fold: 1) gene flow - e.g. resistance genes will be "diluted out" as resistant bees breed with non-resistant bees or bees resistant via a different genetic mechanism, and 2) generation time - bees have 1 or 2 generations/year (e.g. newly established colonies &/or replaced queens); varroa has a new generation every 11 days or so. Evolution takes place over generations, not absolute time, giving varroa a huge leg up on bee's.
In nature, one of three things tends to happen when a parasite/disease jumps to a new species (which is what varroa has done with European honey bees; its original host being Asian honey bees). Either the new target species goes extinct (not a great option for our bees), the parasite files in its species jump (that ship has sailed), or the parasite and its new host co-evolve to reach a less harmful equilibrium. One cannot concentrate on one side of that equation and hope the other falls into place; extinction, not co-evolution, is the more common outcome of these sorts of evolutionary interactions (there is a reason why >99.9% of all species that have existed on earth have gone extinct).
That's not to say that evolution/breeding doesn't have value in the fight against varroa - it does. But its not a panacea, no more so than the chemical & management options available to us. Ultimately, we're going to need a combination of chemical, managerial and genetic controls.