I did some reading up on the instant light charcoal a while back that said if the bag is left open for long periods of time, say months, especially in a hot shed or somewhere hot in the summer months (conducive to evaporation), the lighter fluid the charcoal is soaked in will gas off until there's little left. It originated as a complaint against "Matchlight", the instant light brand available where I live in Ontario, Canada. There is hope to detoxify the stuff to some degree. The other thing I would imagine is those briquettes would have fillers I don't want either, if they're soaking briquettes in lighter fluid they are likely doing other questionable things (using too cheap/tainting processes and materials).
Some people swear they don't taste lighter fluid in food cooked where it was in use, others swear they do. I think the range of lighter fluid taste 'perceived' has to do more with individual palates than the presence of an off taste or not. In particular, a person with a partial or full denture that covers the roof of their mouth will not 'taste' to the full extent they could with a bare palate. I learned this when I had a flipper that covered my palate while getting a front tooth dental implant. There was a huge difference between what I could taste with and without the flipper so I always removed it when eating.