Since anyone can set up their own triple mix business without regulation and there are no controls over what can actually be in it there is no such thing as a strict database of scientific information for this product; MSDS depends on the fact that the products listed are very narrowly defined and consistent.
There have been some efforts to define what triple mix is (see for example this website where the author claims a background in chemistry) but that of course only takes us so far. Once you identify primary ingredients such as topsoil, compost and other materials you then start asking well where did the compost come from? While it might sound organic we bear in mind that some of it might have come from street side pickup from Joe Blow's yard where he insists on zero weeds and indulges in a chemo blitz to ensure that fact. Municipalities are trying hard to recycle stuff, and while they can effectively provide a big machine to chew up and turn the inputs they rely heavily on soil organisms to provide a good end product but in effect just throw it out the door once the hot fermentation is over.
A good source of information is reviews of widely sold products. When you see observations such as a "bag of dirty wet twigs" you are forewarned, and can take comfort when you see warmer reviews flattering the producer.
In my area there is a seasonal business which starts up each spring specializing in bulk soil, manure, peats, compost, stone and so on for landscapers and gardeners. It will probably be easier and more reliable to talk to them than to corporations. They may know the farmer who supplied the manure and a word from him might ease your mind about the quality.
The final word might be that root hairs do the final selection of what goes into a plant. Living things are pretty selective about what they allow to pass that barrier. See this treatment for a detailed discussion of how root hairs work. If you do not have your own garden and only require small quantities, find a gardener who will be willing to supply you directly with soil and insists on taking it back once you are finished with it.