i think that's a good question.
as barbara said, immunity from vaccination is very reliable, though not 100%. If the vaccine was good and given at the right time, and the dog's body is able to mount a normal immune response, then they are going to be immune to distemper and parvo. The AAHA says that this is a potentially valuable use for titer testing, to make sure the dog had a good immune response following vaccination, in order to be more certain and avoid consequences of vaccine failures.
My impression is that, at the dog parks i go to, the risk of infection with parvo or distemper is extremely low to virtually none. there are no reports by long time regulars, who love to gossip about such things, of there ever being any disease attributed to contacts at the park. The owners of the dogs at the two parks i go to are clearly conscientious, and i expect most of them have had their dogs vaccinated, and those who haven't closely supervise and care for their dogs--i've never seen anyone bring a sick dog to the park.
There's another dog park in my area that has a bad reputation as far as dogs not being well supervised, and dog fights being too common, and the place being dirty, so i would think the risk would be higher there. For me, it would partly depend on the condition of the dog park and the behavior of the people there whether i'd worry about it.
Did the woman say why she chose not to vaccinate the chihuahua? To me, there is a difference (in my expectations about the dog's health) as to whether her reason was out of concern for the health endangering possible effects of vaccination, or just being too lazy to take the dog to get the vaccinations. If she just didn't get around to it, i would worry more about the dog's health, while if she made a positive informed decision not to vaccinate the dog in its best interest, i'd expect the dog to be well cared for and more likely to be a healthy dog.
With respect to rabies, in my part of the country, there hasn't been a report of a dog with rabies in years, possibly decades. In the last year data was reported by the CDC, 2001, there were none reported in my state. In the whole US, there were only 89 reported--out of millions of dogs. (if you remove Puerto Rico, the number would be appreciably lower).
2001 incidence of reported rabies in dogs
Because of this and because there isn't even any wildlife rabies reported in my area, i am not worried about rabies from a dog park.
Bordatella or other kinds of kennel cough could be caught at a dog park (LauraD's boy Riley had the unfortunate experience). Bordatella is harder to prevent by vaccination because immunity lasts less than a year but people normally just have it done yearly, the common vet recommendation, and it cant be known with exactness at what time the immunity wears off, between 6 and 10 months i think. So it would be easier for this disease to be contracted by a previously vaccinated dog than the core viral diseases, distemper and parvo. The younger the puppy, the more vulnerable; older dogs usually have mild self limited kennel cough disease, not life threatening, but puppies can get seriously ill and can die.