Open the Record and Run settings window(Automation -> Record and Run settings) and check which radio button selected in the Web tab.
1. When you select the option "Record and run test on any open browser", You have to have a statement in your script to open the Browser and then the "openedbytestingtool" property will be 'False'.
2. When you select the option "Open the following address when a record or run session begins" is selected, QTP will launch a new broswer and open the specified url and the "openedbytestingtool" property will be 'True'.
Look here for more details.
HP QuickTest Professional Add-ins Guide > Overview > Testing Web-Based Applications > Setting Web Record and Run Options