Let me give two actual examples of this to explain the situation further;
Permeate was featured in Australian current affairs media as an additive in milk about a year ago. Much was said about the quality (or lack thereof) of this additive and it was generally pitched as a bad thing to put in milk. Almost overnight pretty much every bottle of milk on supermarket shelves had 'Permeate Free' or some similar variation printed on it. The other day I went to a shelf and picked up a bottle of milk; I caught myself putting it back because it didn't have 'Permeate Free' written on it.
In this instance, the effect of all those bottles of milk having that written on them was NOT to imply that Permeate was bad; the press had already done that. What effect was had was to make me assume that if the sticker wasn't on the label, then the milk probably DID contain Permeate.
In this case, the label is not a fallacy because manufacturers who are being accused of using a poor quality additive are really just advertising its absence which is within their rights given that the press implied that it was almost global in its use within milk supplies around Australia. It is perhaps a matter of conditioning that one infers by the lack of advertising of an absence that a presence exists, but that is another matter.
2) Fat Free Lollies
Many of the bags of lollies in the supermarkets these days proudly sport a sticker proclaiming them fat free. This is not a lie; the lollies which sport this sticker are almost 100% sugar, the remainder being flavouring and other additives.
The fallacy here is that because fat is bad for you, that if the lollies contain no fat, then they're good for you. My personal view is that this kind of labeling is false advertising because it implies that something is better for you than it really is by focusing on the single bad attribute that the product actually doesn't contain.
I don't know the specific name of this fallacy off hand but the description is 'implying that the absence of something bad makes the object good'.
In the case you mention above, the existence of the fallacy (or not) hinges on whether one would reasonably expect the chemical mentioned to be present in product advertising its absence. I (for example) wouldn't actually buy a loaf of bread with a sticker on it 'Free of Crushed Glass!' because what the hell are they even mentioning crushed glass for in association with bread? That the bread has such a sticker on it means I infer that they think that bread MAY contain crushed glass, and I don't want to buy a product off someone who even thinks that's a possibility. For the same reason, if EatIt has only been associated with (say) fruit juice and I see an 'EatIt Free' sticker on a loaf of bread, then yes, Mark's comment to your OP holds true as it is a question of relevance.
If your EatIt (on the other hand) has been linked to loaves of bread, then advertising its absence is NOT a fallacy for the same reason that advertising a loaf of bread as 'organic ingredients only' isn't a fallacy; it's merely refining the list of what the manufacturer has used as ingredients.
As such, there is no distinct fallacy related to promoting the absence of something in a product, but context may reveal a fallacy in other ways.
Edit to address changes in OP
As has been explained further, there is the question of the makers of EatIt and their claims that advertising the absence of their additive in other products generates paranoia.
The fallacy there is quite simple; you're calling into question the claim through calling into question the motives, or character, of those making the claim. This is known in the vernacular as Character Assassination.
This is no better than many other forms of personal attack. "You're only saying that because you're biased" is a common catch cry of many who believe that their claims are so axiomatic, that anyone who doesn't believe them must have some failing of intellect or character. The position of EatIt manufacturers attempts to bring this argument to bear against the advertisers in question.
Another real life example; about 30 yrs ago (again in Australia), medical advice was being given to people with cholesterol issues not to eat eggs, because it would exacerbate their condition. The sales of eggs started to plummet as people who'd been eating them all this time thought they were now bad for your health.
The egg companies when to a great deal of trouble to create their own advertising campaigns that explained the role that eggs play in a typical diet and why they didn't actually cause cholesterol issues. They were largely successful.
Instead of attacking doctors or other medical professionals for their comments, they conducted an ethical and informed campaign of public awareness that explained when and when not to eat eggs to maintain a balanced diet.
In my personal experience, character assassination is employed when those objecting to the original statement (in this case contains no EatIt) cannot argue a more articulate case. This may be because the facts are against them, as is likely the case in EatIt, or when something appears so obvious to a person that they have trouble justifying the belief in the first place. Often statements like 'You're a racist' fall into this category. The person being labelled in this manner may very well be a racist, but this labelling as a fait accomplis to end a discussion doesn't actually add any value to the debate, and doesn't inform the alleged racist on why his world view would benefit from modification.
This point however, goes well beyond the scope of the OP. Suffice it to say that there IS a fallacy being conducted by the manufacturers of EatIt, who would be better served by an ethical campaign of public awareness if EatIt is not the monster the public believes it to be.