Accurate in the way that many mainstream Americans use the definition, yes. But in any sort of Socialist or Marxist terms, no. Socialism =/= state spending or more state control of the economy. Socialism is a social and economic system characterised by social ownership of the means of production and co-operative management of the economy, mostly by workers controlling the means of production. Since this never took hold in America during FDR's administration, it is not an accurate claim.
Just a word of caution: questions involving the terms "socialism" and "capitalism" are likely to be lightning rods for sideways discussion, because these terms are likely to have multiple definitions for different groups and people. I would suggest being very detailed in your question here, about exactly what you mean to ask about. Who made this "socialism to save capitalism" claim? By what did he or she mean "socialism" and "capitalism"? Those terms mean very different things to different people, and they are, unfortunately, terms that tend to be divisive.
Once we have a definite sense of what was meant by the question, we can then apply the facts of FDR's policies during his presidency to the theories as they relate to those definitions, but without them, we are likely to be talking across ourselves, as some people will think of socialism as "entitlements and welfare state," others will think of it as "state control of the means of production," others will think of it as "a Marxist stepping stone on the way to communism," etc. And likewise for capitalism. We need to carefully define these terms in historical and economic context, so I'd advise giving a larger quote for what you're referencing and we can go from there.
It is completly false. By ever interpreation I can think of.
I am tempted to lay out every interpretation that I can think of any say why it not true but its late and its kind of a pointless exersise.
First one has to understand that FDRs policys where not really clearly directed. He did not have a clear vision and a solution. He seamed to have favored a kind of 'throw everything against the wall and see what sticks'-policy approch.
By far the most importent, and 99% of economics would agree, is that the got the US of the gold standard. Now im tempted to go into a huge thing about the gold standard but lets leave it out. Its enougth to say that the gold standard in general is not that bad but in the perticular situation the US had to easy montary policy, and going of the gold standard was one way of doing it.
This did not 'save' capitlaism, but it helped the US get out of the first part of the great depression. Had he stayed on the gold standard, the recession would have deepend probebly for a couple more years.
Not ironiclly it was his policys that got the US in the second part of the great depression (and thereby making it 'the great depression').
I am not 100% sure what the person that invented the phrase meant but I guess it was a old school keynsians who belived that goverment spending during the 'New Deal' pushed america out of the depression. This is a view that by now not even old school keynsians agree with (they shifted to WW2 spending). Almsot everybody else including New Keynsians agree that montary policy is at the heart of it.