I've reached out to chase to ask about this situation (using hertz points for weekly rental, paying tax/fees/options with CSR). Chase via message said they cant answer this and to contact benefits admin.
I then called benefits admin and the rep was very sure it will not be covered, however he said even if one day was paid it would be. So that throws "entire" into a doubt. I asked him to reconfirm that a rental of 6 free+ 1 paid day would be covered for all 7 days, and not just one paid and he went away to check, returning with resounding 'yes it will be covered"....

so there you more inconsistency.