The short answer to the reason why Phase perfect can do what they say is the inverter stage is way over built Vs a single point of use VFD. The reading on Practical Machinist is very informative and features several real world examples of installations similar to your needs.
My shop has 480 three phase service IF I were to move to a location where there was only single phase a Phase Perfect would be the solution. They really are the best way to generate three phase, not the cheapest, at least in the short term. If you look at total cost in the long term thou, I think in power efficiency and quality they win the day.
A rotary phase converter has an idle load value, when you run a rotary the power to spin the converter is wasted. That can add up pretty quickly. For a hobby shop it is not a big deal, in a production shop the constant use of a large rotary is several KW day in day out.