Lily was 81mm at 13+6.
Did they actually say you're only 12 weeks? I could understand your mw saying this as they do go by your LMP, but I can't understand the sonographer saying it as length is how they date it accurately - the sonographer has no idea how far along you are just by looking, but takes the measurements and looks across the grid to find the corresponding date.
My mw told me that the sonographer's EDD is only used if the mw's EDD is out by a week or more - which by the sound of things, yours should be!