I think the amount of fat around your stomach is a factor, of course, but its insensitive of her to be quite so blunt with you (especially as I would assume she's had the same situation a zillion times before!). There are other factors, such as the position of the baby, your womb, fluid, the equipment etc.
With DD1 we only had fuzzy scans (and actually had to have vaginal scans mostly). DD2, where I was actually a bit heavier, the second scan was amazingly clear (the best she'd had all week apparently), almost 3D in the sensation we had. However, she still had to do part of it vaginally, as my womb is quite far back apparently (!). I'm not overly obese IYSWIM, probably about a 16/18, but do have a big tummy. So maybe your 20 week scan will be better - or go for a private scan maybe.
The wording on the form/printout is just standard, don't take it personally.
And congratulations! Assume the scan showed that all was well, which is the main thing!