thisThis was driving me slightly nuts for a min, and I had some projects that would be "modified" as soon as Altium opened it and others which would behave fine.
I dug through the project parameters looking to see what was different.
I found something that fixed this problem for me, hopefully it helps you too. If you go into your Project Options, go to the 'Options' tab. There is a section for "Net Identifier Scope". When this was set to "Automatic", I had the issue with Altium falsely thinking I had modified the project file. When I changed this to either "Flat" or "Hierarchical", the issue went away.