A 60 amp breaker should also ensure no tripped breakers, since there's already a 25% buffer in there(over the 48 the HPWC will actually draw). Heck, I run my HPWC at 48 amps on a 50 amp breaker and it hasn't tripped yet!
I don't think it's a super big deal, but its definitely not kosher. In truth, with this particular equipment there's not THAT much to go wrong that would accidentally have the HPWC start drawing 69 amps continuously, have the breaker not trip, and have the innards of the HPWC or its wire to the car burst into flames. This is decidedly unlike motorized equipment where mechanical things might break and cause unusually high loads.
I see you have put a screenshot of a Gen2 HPWC, which can indeed use a breaker over 60 amps. I guess I just assumed you had a gen3 installed.