After I posted this I investigated the source code and came to the same conclusion as you. BuddyPress does take over WordPress search and causes any other WordPress search (including the inbuilt one) to stop working.
I did however find a work around! What happens is buddypress defines a search slug that is the same as WordPress. What you have to do is redefine the buddypress search slug to something else and your search will start working again.
Basically you want to put the following in your wp-config.php
`define( ‘BP_SEARCH_SLUG’, ‘bpsearch’ );
I tried to load this further up the stack to try and override this but wp-config seemed to be the only place this worked.
You can find out more about how I worked this out over at this post: