You can have Salmonella without actually knowing it, the reason behind this is that there is a group of salmonellas known clinically as non-typhoid Salmonellas (this means they are still S: enteritidis, but different serovars other than the more popular S. typhi). These most of the time cause mild infections as noted by the World Health Organization non-typhoid Salmonella. These infections can even be completely asymptomatic (carrier state) as it has been known for more than 2 decades Old paper on treatment for asymptomatic salmonellosis. We also now know thanks to modern genomic analyses that even within different strains of S. typhi some strains are more virulent than others.
There is even an atlas provided regarding the "less popular" Salmonella serovars, I suggest checking it out if you are truly interested in this topic CDC Salmonella Atlas.
Also regarding your original question there is an useful review here that mentions human-infecting serovars of Salmonella reported in relationship with snakes & lizards A Review of Salmonella and Squamates (Lizards, Snakes and Amphisbians): Implications for Public Health. As you will see the species reported belong to the group that can cause mild or asymptomatic infections so that could be contributing to the fact that people don't have that much trouble with bites from these animals in general. Of course what Stephanie said in his answer is true but also the implicated serovars are less virulent in general than the well-known S. typhi. More in favor on this last point you will see that in the review they mention that some people did develop extra-intestinal disease from reptile-derived Salmonellas like the man who got sinusitis, this means that if the strain is virulent enough in will cause disease even outside the gastrointestinal system.