No, they're not high in fat.
However, they're very high in a sticky fruit sugar that coats your teeth and
pretty much guarantees decay.
Raisins, prunes, and most dried fruit are the same way. Another reason to
scrape your fangs after you eat. :)
OTOH, did you know that black, unsweetened tea helps prevent tooth decay?
I've forgotten the science behind this discovery <s> but I read it
repeatedly back in the 80s. I was glad, since I like black tea