Dogs would do the same thing
A cat bite puts you at risk of several very serious infections which may not develop until much later and can cause long-term consequences.
Dogs do impact damage, but cats do poison damage.
I've read a ton of stories lately about folks who barely bled/hurt and ended up requiring surgery.
The problem with cat bites is that people don't know how they can cause sepsis and kill you within a few days, despite appearing relatively minor. If their teeth penetrates ligament lining, it can totally destroy it, etc.
My doctor told me they'll clean dog bite and send you on your way, but a cat bite they may hospitalize you for days for monitoring, antibiotics, etc. expecting a wide variety of dangerous ailments.