How do we know that mild forms of rabies are nonexistent?
There are many people worldwide who are exposed to rabies and don't die (they get treatment), but there are very few of these cases where people don't die after rabies has entered the central nervous system, and even fewer who didn't receive post exposure prophylaxis before the virus reached the central nervous system. Rabies isn't as rare as many would like to believe, unfortunately, with approximately 15 million exposures and 59,000 deaths a year, so data is available.

"Once symptoms have presented" in the Wikipedia article should probably be edited to "once central nervous system symptoms have presented". As discussed in this review rabies entry to the central nervous system is typically the "point of no return". One of the main challenges of rabies is that the virus hides from the immune system inside cells, making its way from muscle to peripheral nerves to the central nervous system before the immune system can mount a response. Once in the central nervous system, it has special protection from immune surveillance. The goal of post exposure prophylaxis is to allow the body to generate an immune response clear the virus before it gets to the central nervous system.  

Generally, we say that central nervous system rabies is almost uniformly fatal without treatment because that is what has been observed and reported. *I'm not aware of any published epidemiologic survey looking for anti rabies antibody in healthy non-immunized adults. I know it's not very satisfying, but I would strongly suspect that someone has done a seroepidemiologic study and not published these results, since they're exactly what physicians have been taught since before Hippocrates: a dog bite followed by the characteristic illness leads (almost inevitably) to death. Other illnesses, on the other hand are observed to produce an antibody response in individuals' with mild disease. It is possible that there are unknown cases of mild non-encephalitic rabies that are self limited, but given the 150 years of intense study, I don't think it is likely there is a major aspect of the disease's natural history that hasn't been observed and reported.

Re: your idea about dilution of the vaccine suggesting you could dilute the virus, I think you may have a misconception about what that method actually involves. A killed virus vaccine cannot replicate, and so cannot cause rabies (though some forms of rabies vaccines used in the developing world have fairly high rates of nasty side effects). 

Pasteur's risky rabies vaccine trial in 1885 may have involved a live vaccine, but he was notorious for incomplete documentation on his methods. It was essentially, a specimen of air dried rabbit spinal cord that didn't cause rabies in dogs. Here, his method was reported as drying spinal cord segments for longer and longer periods of time until the specimen did not produce rabies in dogs. This isn't a method that "dilutes the virus", but rather a method that attenuates the virus, making it less virulent. Pasteur didn't have methods for detecting what exactly that meant, other than that it didn't cause rabies, but did prevent the animal (or human child) from developing rabies after exposure to a virulent sample.

You can read more about rabies in Murray Medical Microbiology, Ch. 60

*Please see the link in @iayork's comment for a very interesting example of rabies serology in members of two communities in the Peruvian Amazon.