No, Squish tests do not break because of updating Squish. I guess we'd have no customers if that would be the case :-)
The wording there may be unfortunate. What is meant is that you should not just record tests and leave it that way but rather see the recorder as an assistive tool to create tests and use methods such as refactoring to generate stable and easy to maintain scripts.
Something along the lines as you can find in our documentation at http://doc.froglogic.com/squish/4.1/all/tut-qt-creating-manual-tests.html
It is a common, unfortunately wrong expectation that GUI testing means that you just need to record and that's it. Short-term that may be ok and work but long-term this will be not what you want to maintain. So indeed, test automation is a mix of script development and using assistive tools such as recording, snippet recording, the spy, object map, etc.