No, that's wrong. At first they would go by LMP, but once you explain your long cycles they should believe you and/or send you for a dating scan. As an example, if I'd managed to get pregnant on my longest cycle last year and they insisted on using LMP, my "EDD" would have been about a month after I found out I was pregnant.
Having not dealt with this personally, if you didn't get a dating scan would the doctor take your word that the edd is wrong? Or should they automatically refer for a dating scan?