Inability to use FTL Assist

[Lax]

Why would setting Use FTL Modifiers to On make all the key presses include a Shift in the press?

That's the definition of that option. It adds Shift because the FTL Modifier for your Slot is Shift. This option is used by the FTL Assist Me, FTL Target Me, and FTL Follow Me mapped keys in order to follow, target, or assist the correct slot. By separating it onto these specific Mapped Keys, only the keystrokes from these Mapped Keys are modified by FTL, leaving you free to use any modifiers you please for the rest of your mappings.

This is why the FTL DPS Keys generated by the wizard (which are great examples) and any additional DPS keys generated by the Many New Mapped Keys wizard in for the FTL DPS Keys map will automatically perform a Do Mapped Key Action to send "FTL Assist Me" to Window:Current (self). This makes the other windows assist the current window before pressing whatever other button.

If this helps in any way, the FTL Assist Me in the General key map uses key Alt-Backspace.

The Hotkey for FTL Assist Me is Alt-Backspace, but unless you press that yourself, the Hotkey for FTL Assist Me is irrelevant. The assist macro by default is assigned to Backspace, and the FTL will cause it to use Shift, Ctrl and Alt combinations plus Backspace. If the actual WoW macro is assigned to Alt-Backspace (either in the Game Helpers or a WoW Macro Action), then you will definitely have trouble assisting.

With that said, if assisting works manually but not automatically it would help to see your config. Or are you making them always assist one guy?