I think it is good to keep in mind that everything you can touch, see, smell, etc., is a "chemical" or chemicals.
Vinegar is a witches brew of chemicals. Wine, beer, a steak, etc., are all complex mixtures of chemicals. And the smoke we love so well is a dangerous mixture of hundreds or thousands of various chemical compounds, many of which are known carcinogens.
That doesn't mean that we shouldn't try to be safe, and consider carefully anything that will come into contact with our food, or remain on surfaces in the smoker only to vaporize and combine with other things, or break down with heat into toxic compounds, etc.
But I also think people can be bamboozled into believing one cleaner is safe and another dangerous when the reality may be just the opposite. Often, we don't have enough information to make a good call. And the manufacturers will use language to try to make their product seem "safe and natural" because they know that will sell more. But consider the many many "natural" compounds that nature has devised specifically to be highly toxic. Snake venom is "all natural". So is ergot or toadstool toxin, or...
And what will the impurities in a particular run of vinegar (for example) do when heated, volatalized, and combined with smoke, or the surface of a brisket coated with some rub? The fact is, we just don't know, even if the product is called "natural". So I think you're all right when you advise rinsing things off pretty well with water when finished. You don't want water to get down inside of the workings, or soak into the insulation betwen the walls, etc. But a damp rag might be a good follow up.
But I also think we can worry too much, too.
I see that the Simple Green makes a point about not containing any phosphates. But phosphates are exactly what I've found to do the best job of dissolving the smoke residues in my smoker. Good old trisodium phosphate from the paint department of the local hardware store kicks some serious tail on all of these surfaces. Just wear rubber gloves and eye protection to be safe, though, because it really does take the fats and oils out of your skin.
But boy, howdy does a solution of TSP in warm water just destroy that smoke and tar residue. Put a teaspoon of TSP into your dishwasher along with your favorite "no phosphates" dishwasher soap and see what it was those missing phosphates did for you back before "they" made the manufacturers leave them out. ;)
Bring on the (proper) chemicals, brother!