1 in 300 is actually pretty good, given the odds based on maternal age are something like 1/109 for a 40 year old mother. So, your sister has better odds than other mums based on age alone.
I had the 12 week scan and the numbers were something like 1/1800. I'd never bothered with the bloods at 10 weeks for my previous two pregnancies, but got pushed into doing the similar test in second trimester. That came back at 1/24! OMG - how could the two tests be so different? I fell pregnant when 34 (35 now). It was a bit of a shock - we were referred to see a genetic counsellor and the obs and sonographer were all kinda pushing that I do the amnio. I decided early on, that i wasn't going to do anything, so what was the point of risking the pregnancy with an amnio? I'll love our baby regardless. Like somebody else mentioned, we did some extra ultra sounds at 16 weeks and then the 20 week scan. The soft markers looked good and the sonographer was pretty happy (apart from an echogenic bowel - which suggested that it was either down's, cystic, a virus I'd had or the baby had ingested blood from my 2 week bleed in first trimester). Great, so we ruled out cystic with more blood tests and apart from that, I'm not stressing about it. I think with my odds of 1/24, it's something like a 4% chance out of 100. So, 1/300 is much, much better.

Tell your sister to go with her gut feeling over everybody else's opinion/s - whether to do further testing, whether she 'feels' that there's anything wrong and what she would do if the amnio results came back positive. And the Dr shouldn't be saying that she 'needs' to do the amnio. It's totally up to your sister as an option, if she chooses.
I think I've been a lot more relaxed about all of this, as we had genetic testing whilst pregnant with DS2 as I'm a carrier for spinal muscular atrophy and my cousin's first girl died from this, so down's risk was nothing compared to the stress of my previous pregnancy. Just trying to put it into perspective.
Good luck and hope everything works out well for your sister!