Indeed, Diners Club always argues against loss of use on my behalf and has so far always won with Avis. Only had to pay an administrative fee of $100 the last time (no administrative fee before that). And it's always primary.

However, if someone (in the US/Canada) doesn't already have a Diners Club card, it's immaterial, because you still can't apply for a new one (and it may be a long time yet before you can, given the snail's pace of the transition of Diners Club North America from Citi who sold it to Bank of Montreal/Harris Bank who bought it).