In most places, regardless of financial liability for damages, a dog bite incident is handled the same regardless of where it occurred or circumstances. If your dog bit you in your own home, and you sought medical attention, it would be reported to animal control and handled the same by them as if your dog was running loose in the street and bit a stranger, for example. People often erroneously conflate who is financially or criminally responsible for damages resulting from the bite with whether or not the DOG faces consequences for it.
So, while in many places (though not all) you would perhaps not be financially liable for the damages if the other dog entered your yard and your dog was appropriately contained to it, a bite incident is handled as a bite incident in most places, regardless of circumstances. Yes, it is "fair". Regardless of the location where the bite occurred, your dog has a long history of attacking other dogs, and you have a long history of failing to take reasonable and prudent action to prevent it, and so your dog is an established risk to others while in your care.
This has happened MULTIPLE times. You were clearly WELL AWARE of the potential consequences for your dog if it happened again. Why on earth would anyone who cared at all for their pet not take significant steps to 1) secure their yard so other dogs can't enter and 2) not leave their dog out in the yard unsupervised?