I'm just putting this here just in case anyone else is looking for it like I did.
Changing the default text which gets placed in the search box does not require re-filtering the entire search box wrapper. There's a filter which I couldn't find in the docs and so doing this:
//Change search box text
function childtheme_search_value() {
return "Enter your changed text here..";
}
add_filter('search_field_value', 'childtheme_search_value');
will let you change it whatever you like :)
Hope that helps someone.
