That is incorrect. Anyone can take any car into the US. The restrictions are that a Canadian can not take a US-plated car into Canada, and probably not do a roundtrip rental with such a car.
However, Tuneman will be doing a one-way from Toronto to Chicago. If it were to a traditional "border city," like Buffalo or Detroit, the rental companies might give out a regular Canadian-plated car, since Canadians one-waying back to Canada will need it.
But for more distant US cities, where one-ways to Canada are likely not that common, a Canadian-plated car will sit unused. I'm pretty sure it can not be rented roundtrip locally, since it was "imported" from a different country. So the rental companies want to give a car with US plates.
If it were Hertz or Avis, they'd say fullsize reserved one-way to Chicago, need something that came one-way from the US, take this ratty old Impala with 35k mi and NY plates. Don't like it, tough luck.
In this case, the problem is that National has a "vehicle choice" program, with a possibility of free upgrades by choosing from a designated row of parked cars. So people with elite status, like Tuneman, reserve a fullsize, and often want to snag an upgrade to something bigger, like an SUV. If he takes an SUV from Ontario to the gate, the guard may stop him and say, wait a minute, we need to find you something with US plates, so you don't have a choice today.