If you spur from a ring in the house to the garage and then installed a small CU in the garage, any problems in the garage can still trip the RCD in the house CU. You'd lose some or all of the electrics in the house as well as the garage so that's very inconvenient and certainly doesn't provide 'garage protection self contained within the garage'.
The 13A fuse on the ring can blow for sure, but unlikely as lower trip values are inside the garage. As the garage piggybacks the ring if the ring drops out so does the garage of course, which is far from ideal.
I didn't mean that the FCU on the ring would blow, I'm saying the house RCD will trip and you'll lose all power to the house and garage. A faulty appliance in the garage or water ingress or earth leakage etc will trip the house RCD which will be very irritating to family members. Also if you have a high load in the garage (but not so high as to trip the garage MCB) and people in the house are using the ring then that would make the MCB on the ring trip.