Can you supply the links to these "MusicBee docs and FAQs" you mention?
Your question is of course legitimate. But at this moment in time, x86 software will run perfectly on Windows x64.
Have a look at your C:\Program Files (x86) folder.
I would be very surprised if there are not a lot of entries from lots of programs, all running 'under x86' perfectly.
A reason for sometimes even deliberately using the x86 version instead of the x64 version of a program is that some add-ons or plugins for that program simply won't work under x64. (Adobe Photoshop, MediaPlayer Classic, etc.)
Until only very recently, for many years even Microsofts own advice was to use it's Microsoft Office software in the x86 version on Windows x64.
The x64 version was not preferred, nor advised.
For some software using very large amounts of memory (e.g. video), or perhaps for security reasons x64 might have advantages, but for most software at this moment I believe there is hardly any need or advantage to have an x64 version running.
Just google for some wordings such as "32 bit vs 64 bit software" and you'll get lots of useful information on this subject.
And again, please post (or preferably PM me) the links. I can't imagine they are legit.