I haven't heard that podcast, and I haven't read Picketty's book, but that assessment of the effects of the early industrial period is basically correct--or, at least, it represents the broad scholarly consensus.

I commented at length on this question, and what is called the "Standard of Living Debate," at some length here. I encourage you to read that whole string of comments, but I'll quote a bit below:

This is built around the "standard of living debate," which took its "modern" form in the 1950s and 60s, in no small part due to the work of Eric Hobsbawm. The basic question is whether or not the condition of the working classes improved in the early industrial revolution, traditionally dated from 1760 to 1820 (the reign of George III) but later expanded somewhat to 1750 to 1850. The debate centered for decades on "real wages," the ratio of nominal wages to a cost-of-living index based on a hypothetical basket of goods. And, if you look at these indicators, as people like Jeffrey Williamson made a career out of, it turns out that real wages actually appear to improve quite rapidly. This led, by the later 1970s and early 1980s, to the temporary triumph of the "optimist" case (not surprisingly coinciding with Thatcherism), over the "pessimist" case. The optimist case held that real wages got a lot better quite quickly, and thus industrialization, capitalism, and the free market were all Very Good Things. For example, Williamson and Lindert argued in 1983 that real wages increased 80% from 1820 to 1850.

But...

Starting in the 1980s and then really building through the 1990s, the pessimist case began to regain ground, and it is now the more convincing of the two. It began with N. F. R. Crafts's reassessment of macroeconomic growth, in which he found that growth was considerably slower that previous historians (e.g., W. W. Rostow) had argued. This is problematic for the optimist case, because if the economy as a whole isn't growing rapidly, and we know that there isn't a great redistribution of wealth happening, then how are working class real wages improving so much? A range of further studies of wages and prices also chipped away at Williamson's original numbers, each time revising the apparent growth in wages downward. It's to the point now that estimates for real wage growth from 1750 to 1850 are quite modest. Feinstein argued in 1998, for example, that real wage growth from the 1780s to 1815 was practically nil, and that wages in 1850 were less than 30% higher than in 1780. The real clincher, and the most interesting aspect as far as I'm concerned, is the expansion of the topic beyond wages and prices. The early framing of the issue was so heavily economic and quantitative that it dominated the conversation for decades. However, it's easy to forget that that original quantification in the 1950s and 1960s was in fact an attempt to support the qualitative evidence that already existed, and which was unambiguous about the conditions of the working classes in early industrial Britain: it was terrible.[1] Contemporary observers like Friedrich Engels and Edwin Chadwick, and historians like E. P. Thompson had long held that early industrialization was a traumatic experience of long hours, filthy cities, starvation wages, and brutal repression. For them, broad improvements in the condition of the working class only came with legislative change and labor organization: things like the Factory Acts and the development of sanitation infrastructure in new cities. In other words, improvement came after state intervention, not via the magic of the free market. [2]