If done "properly" it can be a much cheaper, quicker and overall easier method. However, there are many ways to screw up, so to speak. In fact, when doing some pilot testing, we had some outrageous results with saliva testing.
For example, we had a group of 4 guys. Well, according to the saliva samples we submitted at baseline for testing, they were all (some many times over) in the supraphysiological range. That just isn't possible. As things continued, we found more and more odd results.
In short, there are many ways to skew results. Blood in the saliva, bacterial count in the sample, dilution of sample, and improper storage (that is a large one). In terms of the storage, studies have shown that by not storing the sample immediately at a temperature of -80 degrees Celsius one can greatly compromise results.
I didn't have time to look at those specific sites but I'm assuming most have you follow the same protocol. You could give them a try and see how things turn out.