Not sure why it wouldn't be "read" by a standard floppy drive...the Tandy would have to have i guess a firmware modification.
A standard 3-1/2" floppy drive is controlled by the BIOS. the BIOS knows how to read two formats natively: FAT12 720K and FAT12 1440K. There is some hardware in the floppy drive itself for these two formats (witness the hole to determine if a disk is 1440 or 720K).
However, even if it did know how to read- say, these disks- it still wouldn't know it was reading one of those disks. The only reason it can even tell a 720K disk and a 1440K disk apart is because of the hole in the disk itself. I have a old 3-1/2" floppy somewhere which replaced the "sensor" that detects the hole with a hardwired switch. putting the switch in "720K mode" with a 1440K disk caused a "General Error reading Drive A" same in the other direction.
However, the floppy drive can of course be controlled directly by software. In the case of a Macintosh disk, which uses a 800K HFS format, the application takes complete control of the floppy drive, and since the software knows how to make sense of the disk format and what the floppy drive gives it back, it's possible to read it.
a tandy-100 disk is a 3-1/2" disk, but just because it fits in the same drive doesn't automatically mean that you can read it. Just as you don't expect to be able to read a DVD in a CD-drive it's unreasonable to assume that just because the shoe fits, it should be comfortable.
One analogy that might make sense is to think in terms of applications. Microsoft Word, for example, can read say, crysis save files, but it can't make sense out of them. a 3-1/2" standard floppy drive might be able to read a Tandy disk, but it can't make sense out of it, and the built in floppy driver on PCs isn't going to be able to help either. Thus the need for proprietary software.