I can't understand so-called grown-ups who can't just decline something without making a drama out of it, or need to justify themselves.
Calling someone "manipulative" because they offer cake? Seriously? Just do what you would teach your own kids to do! "No, thank you." Done.
Bullying and coercion can come in different formats. Just as one bully might demand you give them money to control you, another might try to force you into eating something that you don't want. Offering cake and accepting a 'no, thank you' is all great, but repeatedly insisting and trying to force is appalling controlling behaviour. It's just another way in which people count on your being too polite to offend them, as they shamelessly offend you.
I completely agree that inventing a fake medical condition is not a good idea - if you claim a gluten allergy and she makes a GF cake 'especially for you', she'll be even more forceful that you must have some 'after all the effort she's gone to for you'. Plus, that then makes it difficult if somebody later offers something around that you do want, that you couldn't have if you did genuinely have the condition.
I was also thinking of saying something like "Ooh, no, thanks - every time people bring home-made cake in, it always ends up giving me the raging squitters and leaves me rushing off to vomit every half hour!" (assuming that she's the only person who ever brings things in).
Either that or ask excitedly what that teeny, tiny delicate little decoration right in the middle of the cake is. Then, when she says she can't see anything, insist that it's there as she lowers her head to look more and more closely - and then, when she's a few inches away, shove her face right into it and shout "STOP TRYING TO FORCE ME TO EAT CAKE!!!" 
Seriously, though, I would do as PP suggested and double it back on her. Insist in the same way she does to you, that 'just a small piece won't hurt' and 'life's too short not to treat yourself'. I do feel for her if she has an ED, but it's absolutely not on for her to ride roughshod over everybody else's needs, preferences and potential food issues/disorders.