I can speak to your original question, but not to your rephrased one, as my interest is in comparative economic development so I don't know much about the details of US policies.

It is, in general, very hard to rigorously explain the economic history of a particular country at a particular time (with some exceptions, e.g. a war raging across the land sucks, hyperinflation sucks, the modern Saudian economy is about oil, etc). My guideline is that if it's using maths more advanced than what I learned at primary school, I'm skeptical.

In part, this is because in any sizeable economy, at any one point in time, a myriad of different things are happening, so it's quite possible with a bit of ingenuity to explain nearly any change by pointing to something other things that changed at the same time and make a very plausible sounding explanation, but then it turns out that these things applied to a different economy at the same time, or the same economy at a different time, but the outcome was quite opposite.

Another part of the problem is that economies aren't static. If something changes then people change in response to it, for better or worse. 

Therefore economic history of the type that seeks to explain the impact of the New Deal in the USA depends on assumptions about what would have happened in the absence of the New Deal - the counter-factual. A counter-factual introduces a fair bit of subjectivity. And that subjectivity results in immense arguments when it comes to questions that are politically polarizing, like government spending, everyone agrees that governments fail and markets fail but we all start with our own priors about which ones are more likely to fail, and discussions get highly heated fast. And even summarising the debate can be hard.

Conveniently, in 1995 (a few years ago now), a survey was done of economists and historians who were members of the Economic History Association. In this survey, they were asked to agree or disagree with a number of statements about US economic history, including the statement "Taken as a whole, government policies of the New Deal served to lengthen and deepen the Great Depression", found that 27% of economists agreed, and 22% agreed with provisos, while only 6% of historians agreed, and 21% agreed with provisos. So we can say with some confidence that in 1995 economists and, to a lesser extent, historians were divided on the question.

Less conveniently, to the best of my knowledge no one has carried out a similar survey since 1995. And there has been a bit more academic research (I've added a couple of papers in the sources) directly on the topic and of course much more research on government interventions more generally, which might well have changed opinions on the New Deal specifically. 

So, I think your friend's confidence is unwarranted. But I'm not confident about that. :)

Sources

Robert Whaples (1995), Where Is There Consensus Among American Economic Historians? The Results of a Survey on Forty Propositions, The Journal of Economic History, Vol. 55, No. 1 (Mar., 1995), pp. 139-154 (https://www.jstor.org/stable/pdf/2123771.pdf)

Harold L Cole, Lee E Ohanian, (2004) New Deal Policies and the Persistence of the Great Depression: A General Equilibrium Analysis, Journal of Political Economy v112 n4 (200408): 779-816

Hannsgen, Greg; Papadimitriou, Dimitri. (2010) Did the New Deal Prolong or Worsen the Great Depression?, Challenge (05775132). Jan/Feb2010, Vol. 53 Issue 1, p63-86. 24p.

This is not an answer, so I hope the mods will allow it. I was wondering if you could provide a link to the economist article so we could see what kind of sources and thinking the author used to frame his argument?