Curiousity question:
Back in the day, there was an option in TestComplete to specify, for a project, what a "Main" routine was. This was in the days before "TestItems" were introduced and, even for a while after that, they had some backwards compatible support for those of us who were upgrading to newer versions.
How long as your TestComplete project been in existance? It ALMOST sounds like that option got set somewhere and, therefore, no matter what you do, TestComplete executes that code. If it's scattered across ALL your TestComplete projects, it might even be something in the registry or in the TestComplete settings on your user account somehow.
Have you tried having another user on another workstation attempt the same thing? Are they experiencing the same problem? If not, it MIGHT be worth an uninstall/reinstall on your machine to reset any strange settings.
Another thought:
Are there any command line parameters that are used in running your instance of TestComplete? For example, are you running the project by double clicking on an ICON and then, after it runs, it's left on screen for you to edit? It MIGHT be worth investigating something on those lines as well.
Grasping at straws, I know, but this is a weird puzzle and, as Sherlock always says, "Once you eliminate the impossible, whatever remains, no matter how improbable, must be the truth."