It's certainly not a statement which comes from nowhere so credit where credit's due but I just don't believe for a second we can consider this to be true.
It is well-known these days that peace is the fastest way to promote scientific progress. I could write all day on this but ill try not to...
The first thing we need to remember is that science produces techs and military techs do little to beneift the everyday Joe. In wartime most of the scientific progress brought the Germans techs with military applications.
Secondly, the Nazis were close to finishing one or two famous weapons and we're working on things we don't even have today - but they also made lampshades out of human skin and so unlike in most cases, here i think its safe to say that some of the techs they were working on were not techs which would later surface organically during peacetime.
Lastly for now at least, the US took most of the useful sientists in after the war, spared them the trials and put them to work in the US under a false identity. NASA's space programme famously owes a lot to such men.
A lot of the scientific advancements by the US and her allies since WW2 were indeed based on something the Nazis were working on, but they did not complete most of them and credit should go the US.
The only fact i can think of which would in some way counter-act this, is that the Nazis had access to human testing of whatever they wanted. However, ethical issues aside, whether or not this is even useful to science is debatable.
Peaceful countries such as in Scandinavia were also making great strides in and around that time also. There's little that's significant enough in our memories though to immortalise their efforts a la the Nazi science programmes.
I'll leave it there as i have a tendency to write too much lol