Not wrong at all, mortgage companies can set their own definition of FTB as its their prerogative to do so. As far as HMRC is concerned if you sign a declaration that you are a FTB* when you aren't so that you can avoid Stamp Duty then you would be, by current HMRC definitions, committing fraud.
*as in the case of the help to buy scheme
We were completely open about out history to everyone and we still qualified for the London help to buy scheme, so it seems like they were bending their own rules then