Yes, food industries should be allowed to fund health studies but they should be very upfront about where the funding came from. There is no reason a company with money should not invest in a study. However, consumers need to be very aware and our kids need to be taught to be critical thinkers who can consider the validity of the study.
Most of the diseases people have today are as a result of poor eating habits or too much chemicals in processed food; food is the cause. For this reason food industries should be compelled to fund health studies. Sugar industry should shift blame while we all know what sugar does to our bodies.
Even though it might create some doubt as to whether the study is legitimate, food companies should be able to fund health studies, because it's still better than the study not being funded at all. It might be that they want to hide information about how their products are bad. The might just want to make their products healthier, though.
The food industry should be allowed to fund health studies because it helps them to understand the science and health consequences of the food it produces. It also helps to allocate blame and or responsibility where necessary. Of course, the consumer must be careful to understand what the studies mean and interpret the results accordingly.
The conflict of interest in these cases makes the reliability of such studies extremely questionable. Today, most anyone can write anything on the internet and claim that it was the result of scientifically sound and reliable research. This is especially easier for big industries with a lot of money. One of the only solutions to these problems is for readers/viewers to begin questioning the motives of the creators of such articles/videos because it often does not suffice to look at the sources as there are many "professionals" out there who are willing to stick their names on research regardless of its reliability.
Why should we allow food companies to fund investigation. Remember when all the tobacco companies were allowed to fund their own studies. They were well aware that the were not good but they told everybody that smoking was good for us. Years from now we will look back at this a think" WOW how we let that happen"