I'm not sure if there is a configuration for sensitivity. However, you've demonstrated yet another reason why simple record/playback means of automating tests is a means, not an end. You can use the record feature of any tool to get started in automating a test, but the best tests and the ones that are the most robust, meaningful, flexible, reusable, and transportable are those that have some manual work done to them in editing, removing "extra" stuff, inserting logging events, etc.
In short, unless someone comes around and says that, yes, there's a way of turning that off, it is a "best practice" to always do some judicious editing of your recorded tests in order to help them run best.
