The author of the package confirmed there was a bug (albeit a silly one), and a fix will be pushed out with the next update.

@Markiyan Hirnyk Of course, we can just compute the complex solutions and grab the real ones; that's not the issue I raised.  In my original post, I was able to find the root using Isolate with RegularChains.  My question is why don't fsolve and Isolate work as described?  It would be easy for someone to get incorrect results if they aren't careful.

@acer I did not know fsolve invokes RootFinding:-Isolate with RealSolving by default for real polynomials.  Is this in the documentation somewhere? I couldn't seem to find it.  Though it is very good to know.