Do you have some dynamic content? Like a text variable which is displaying date or time?
The "Date Modified" date is changing in the operating system file listing window.
The date should not change if all I'm doing is opening the file and not make any changes.
I've tried this experiment with InDesign 10 (CC2014) on my MacOS 10.9.5 system and do not see any changes to the OS modification date for the file. Same is true under Windows. And I tried doing some suspicious operations to the document such as printing and PDF export. Closed the document and checked the File Information. The Modification Date did not change. And it normally would not change unless you explicitly save the file. Anything else you are doing while reviewing the document? Again, we would like to help, but can't repeat your symptoms.
BTW, an experiment to try is to “lock” the file using the MacOS Get Info dialog and then repeat your experiment. When opening the document in InDesign, you will see the window labeled as “read-only.” What happens when you subsequently close the document and look at the file modification date?
And of course, I assume you are not confusing the file modification date with the “last opened” timestamp!