To take Ashley as an example. This name suddenly started ramping up in popularity in the 60s. In 1970, there were 927 girls named Ashley in the U.S. It peaked at 54,856 in 1987.
It became notably more popular for boys at roughly the same time! The peak of M Ashley was in 1980, at 746. (Note: it's also very likely that these numbers are wrong. The SSA data also has 56 male Marys in 1980, which is likely the result of coding error.)
Meanwhile, in 1945, solidly in the time period when the article would like you believe that Ashley was solidly a boys name, there were 57 M Ashleys and 10 F. 1950 was 55 M/15 F. Prior to 1960, a "good" year for Ashley was around 100 total babies, with some split of both M and F.
To me, a more honest interpretation of this data is that Ashley was a somewhat unisex, but mostly just very uncommon, name that suddenly became trendy in the 1960s, especially for girls but also for boys.
It did fall in popularity much faster for boys than girls, perhaps as it became to be perceived as feminine due to its popularity for girls. But note that even today, Ashley is still used as a boys name! There were 69 M Ashleys in 2009 and 27 M Ashleys in 2025 (by which point the prevalence of coding error is much lower -- M Mary has fallen out of the data set entirely).
The 2025 F:M ratio of 1829:27 is pretty high, so it's fair to say that Ashley would now read as feminine to many Americans (but note, still less so than Mary). It's much less clear to me that you can conclude from the 1945 M:F ratio of 55:10 that it was once a boys name.
Edit: I noticed that the "How we measured it" notes at the bottom mention this shape for Ashley. But I want to note that it's not unique to that name. Dana, another well-known example of "girls name that used to be a boys name" is very similar. Suddenly trendy in the 40s for both boys AND girls, relatively unisex and uncommon for both prior to that, with usage for boys dropping off relatively quickly as girls' usage continued to rise.
Likewise for Lindsay -- suddenly trendy (this time just for girls) in the 70s. Before then, fairly unisex. 1950 has F:M ratio of 116:97.