After being helped by Ken who was kind enough to "look under the hood" to eliminate any other issues on my system it seems there might be a bug in the latest stable version of Moodle 3.4.2+ (Build 20180512), or at least when running on a Centos 7 server operating system with PHP version 7.2.5 and mariadb database version 5.5.56. The bug I have involves the File Picker's not working when trying to choose a file using Choose and giving it a name in the File Picker box. All I see when doing things this way is a spinning file-upload wheel where the file never gets uploaded, at least not in my lifetime. On the other hand, in drag-and-drop mode the same file has no problem being uploaded with the horizontal progress bar showing progress as usual.
Anyone else out there ever run into this problem?