I think your summary is obscuring some of the nuance in that data. What it shows is that independent voters self-identify as "lean rep"/"lean dem" based on their approval of the current president, which is low right now. Historically though, self-identified independents lean dem more than they lean rep (data in your link). Consider that the last time a Republican presidential candidate won the popular vote was in 2004, and before that was in 1988. It's well known that conservatives tend to vote Republican, and also tend to have much higher voter participation rates than progressives, so if your belief is that there are more Republicans and Democrats, you would expect to see more popular vote wins in elections with generally high participation (relative to other American elections - obviously American voter participation is dismal overall). So what accounts for that discrepancy?

It's also worth remembering that unaffiliated is the largest group, and has been growing. Lots of partisans like to poopoo the idea that "independents" exist, and claim that they are just closet-partisans, but I don't buy it. Massive distrust of politicians and establishments is not something people are faking because they want to fake their stance on the internet.

Anecdotally, people who consistently vote for Republicans are less likely to identify themselves personally as Republicans than in the analogous Democrat case. (The media made "Republican" a dirty word, but didn't really change anyone's mind.)