Still confused.
When you change anything in MC for a given file, the info (tags) can be saved in 3 places:
1. in MC database ("Library") (always saved)
2. in the media file itself as an ID3 tag embedded in the file (this is what that option disables)
3. As a Sidecar.xml file saved next to the original file (this is to prevent modifying the file itself, and also to support file types that do not support internal tagging)
If you use other applications besides MC, you need 2 enabled because they will then see the same changes as you do in MC, and MC will also see changes you do in them.
Options 1 or 3 are only understood by MC, so changes will not be visible elsewhere. This is fine if you only use MC.
"Update tags (from Library)" will copy the information from 1. to 2 (updating the files)
"Update Library (from Tags)" will copy the information from 2. to 1 (updating the database/library)
With 2. disabled, nothing is ever written to the media file so the timestamp does not change.
Note that simply playing a file causes the [Number Plays] to change - if writing is enabled for that field, then the file timestamp will change each time a file is played.