While there are quite a few delivery methodologies and many company adopt their own, the main players are Waterfall and Agile.
Test automation is usually starts when development of new functionality is completed. Commercial automation tool dependent on the GUI and if latter is not implemented, automation simply cannot be started. That means that automation is often done later than it really needed.
Having said that, late implementation of automation aligns well with Waterfall methodology where it will be just another stage (implemented at the very end of cycle). Based on that commercial tool is a tool of choice for Waterfall software developement life cycle.
On the other hand, automation is an integral part of a scrum development methodology. Tools like Selenium or Watir widely used to test the functionality in a web based applications. The flexibility and power of those tools allows often bypass the GUI and/or quickly add new automation code when certain feature in AUT is completed. That makes open source tools very suitable of Agile methodology.
It does not mean that application of open source tools is limited to Agile only. It can be implemented in Waterfall as well. It just makes stronger case to be used in Agile.