Why not back up a Photos library on an external HD using TM?

Apple says don’t do this b/c problems with permissions that my conflict with those for TM. Isn’t there a fix?

I recently managed to rescue my old, large iPhotos library (9.6.1. 19,200 photos) from a failed HD, transfer HD data it to a new external HD, and upgraded it to a Photos library that I can view and work with on my MacBook Pro (2016. 11.4). 

All good, but then I was going to back-up the MBP and external to my 2Big NAS. Until I read this on Apple website:

If a Photos library is located on an external drive, don’t use Time Machine to store a backup on that external drive. The permissions for your Photos library may conflict with those for the Time Machine backup.

My Photos library is too large for the MBP. It must be on an external HD.

I am the only user of my computers. I have never encrypted a file or limited access to file, folder, or photo. Yet I occasionally am denied access to my own work b/c I don’t have permission. Permissions totally escape me.

Last thing I want to to backup external HD with Photos library and provoke another permissions conflict.

Suggestions PLEASE.