I am certain that it is wrong to say categorically, without detailing what one means when one says that biodiesel is non-toxic. Even apart from the fact that you are generalising on several items: mode, temperature, duration of exposure, plus even more pertinent: on source of oil (what plant it is coming from, and which part of it) and whether it is a methyl ester or ethyl ester. In my view it is irresponsible to say categorically that biodiesel is non-toxic.  If you insist then you can sign on the bottom line, if anyone comes to harm from biodiesel of any source and in any application you'll take the responsibility, but I don't think that you would be foolish enough to do that.

As an example: The toxicity of erucic acid (see WP under that title) a component of some canola oils and several others is a contentiou issue. Canola (rapeseed) oil is classed as high, medium and low eruc canola oil and only the low erucic acid canola oil is accepted universally for human consumption.

If you study a textbook on vegetable oils and fats you will find that the composition of an oil can depend on which part of the plant it is coming from.

Another example of the danger of generalisation: Is rhubarb toxic ? Its roots are not, but the leafs are deadly. So if you insist on leaving the statement in, then please say what you mean exactly (which biodiesel, when and how)    

  

Another ex 

The way that this statement has come about (at least two decades ago) is by somebody who wanted to flog the idea of ester fuels, and then it was repeated without thinking.