What are reason logic hooks would work for Admin but not regular users?

Amy, 

Could you please clarify whether you refer to Web Logic Hooks or regular Logic Hooks?

I would suggest making a test.

Here is a very simple Logic Hook configured in Logic Builder from the scratch - it creates a new Note for the Account on Account save
It works for any user and Sugar - Cloud or on-premise, starting version 7.2 and for the regular user with regular access to both Account and Notes modules.

here is the zip package for  this logic hook configuration:
z20210207_flowchart_lb60200d671dbd49_68799798.zip

You may install zip with Module Loader then try out saving any Account with regular user credentials - if you find a new Note for that account on account saved, then Logic Hooks are definitely operational on your instance.

When the test is done, you can uninstall zip with Module Loader.

Amy, 

Could you please clarify whether you refer to Web Logic Hooks or regular Logic Hooks?

I would suggest making a test.

Here is a very simple Logic Hook configured in Logic Builder from the scratch - it creates a new Note for the Account on Account save
It works for any user and Sugar - Cloud or on-premise, starting version 7.2 and for the regular user with regular access to both Account and Notes modules.

here is the zip package for  this logic hook configuration:
z20210207_flowchart_lb60200d671dbd49_68799798.zip

You may install zip with Module Loader then try out saving any Account with regular user credentials - if you find a new Note for that account on account saved, then Logic Hooks are definitely operational on your instance.

When the test is done, you can uninstall zip with Module Loader.