Sergiu, you are correct that if you turn off Stop on Error in the playback, without subsequently setting Stop on Error for the individual Test Item, that TestComplete will continue after an initial error occurs. The confusing thing here is that there are TWO places to specify Stop on Error.
The first place, you know about; in the playback settings for your project. If that setting is checked, then the individual test item settings for stop on error are ignored.
There is, however, a second place where you can specify that the test should stop on error and that is on the Test Item page. On the test item page, there are two columns, one for Stop On Error, and one for Stop on Exception. These two columns are (stupidly in my opinion) hidden by default, which is why I said you need to use the Field Chooser to expose them. Once you can see them, you can set each individual Test Item to stop its own execution, or stop execution of the entire project.
Here is a picture of the setting I am talking about.
