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He mentioned the use of indirect cycle nuclear engines, which means doing exactly what would be desired to avoid circulating compressed air directly through the reactor.  His idea was to resurrect a dead ANP concept of using heat exchangers that circulated molten lead through a pipe to isobarically heat the compressed air as per typical Brayton cycle fashion.  Sure it is a heck of a lot more complex than the direct cycle that was actually tested for ANP but the radioactive materials shouldn't be leaving the reactor in that design.  As a result, the typical layman's belief that it is unsafe by having the term "nuclear" in it might be rendered a bit less logical.  Still, you do have a point that a nuclear reactor with a huge amount of shielding and indirect methods of energy transfer would be quite complex and maintenance heavy, but still it would probably be the only way to make something that has the range to be a viable "hover carrier" without trying to delve into ultra-novel fusion concepts that aren't anywhere near the same developmental stage as regular fission ideas.