I would, and I actually was allowed to bring this upstairs, so I'll use it as an example.
This is a product I found in my own office at the Canadian Cancer Society. Our administrative staff had been using it to clean our whiteboards for a while. As I grew familiar with this file and started looking at different carcinogens, I became more familiar with the names of carcinogens and what they all meant, so now of course I'm a little bit obsessed with looking at product labels.
First, I was shocked at seeing how many different labels are on this one. You can't see from here, but there's a flammable symbol, there's a skull and crossbones, and there's an explosive symbol. Below that it says “extreme danger”. If you turn it around, in small print—it makes me feel as if I'm getting old too—you can read why it has the skull and crossbones symbol on there. It's because it contains tetrachloroethylene. Under IARC, the International Agency for Research on Cancer, that is categorized as a 2A carcinogen, which means it probably causes cancer.
If IARC were able to do more research on humans, which of course it can't, ethically, it probably and very likely would be categorized as a known. Because there are ethical conditions and restrictions around doing research on humans, the evidence is restricted, so they often end up being 2A, which means there's sufficient research that it's cancer-causing in animals and some evidence that it's cancer-causing for humans.
To get full circle to answer your question, when a consumer has purchased this product, decided they're concerned, gone on the Internet, researched, they can finally—sometimes, not always—find what's called a material safety data sheet. On that sheet, they can then read more about that chemical. For this specific chemical, if you have the Internet and if you have the time and everything else, you can read about the fact that this product contains a probable carcinogen, and you can even read about the types of cancers that might develop because you've been exposed to this product.
To summarize, it's not that the data are not out there. The data are available in many, many cases on these material safety data sheets. If you're in an occupational exposure, you can read—although even with that there are big, big, big problems—and find out more about what you're being exposed to. So I would refute the claim that it's as difficult as people claim it would be to tell us about what we're being exposed to and what it potentially might lead to in our futures.