As general word of caution: is that extra fraction of interest worth the hassle/risk of dealing with a less known bank?
What I mean is, banks like Ally offer both near-highest interest rates, are well established, and provide a nice experience. Your savings account is bread and butter in your financial life. Using some "janky" bank just to squeeze few dollars probably isn't a good use of your time.
I'm not saying mysavingsdirect.com is "janky"; I really have no idea about them. But I've seen a number of higher interest bank accounts and turned them down because they were from unknown vendors.
As an example, I was pissed at Ally and needed a new vendor. I decided to try Discover Bank, figuring they'd be good with a well established reputation like Discover, and with the same interest rates as Ally. But the experience has been decidedly worse. Slower deposits and transfers, for example.
Also worth noting that usually you shouldn't be carrying a lot in savings anyway. Excess cash should be sitting in investments and doing work. So savings accounts will only be carrying emergency funds et al. If you've got, say, $12k in your account, an extra 0.4% is only going to give you a few extra bucks a year.
Is a few extra bucks worth working with a lesser bank?
Or, to the focus of the original article, is a few extra bucks worth working with an uninsured bank?
I advise extreme caution when it comes to savings accounts, which are explicitly for "safe" money in a health financial portfolio.