I don't think you need any "add-on". My Office 2007 is able to read all previous versions of Office files.
I believe there are add-ons /modifications to the 2007 version that put the older UI from 2003 into 2007
Either way Access is a special beast when it comes to file types since it isn't an "access" data base it opens but a Jet Database, whose format is determined entirely by the version of the installed JET database engine installed; Each version has a different Database engine version included with it.
However after installing Access 2007, if the DAO libraries are binary compatible with the previous versions (and I see no reason why not) then it's likely that Access 2003 will also create Databases using the newer engine, making them unreadable to a "pure" 2003 install.
This is where the re-registration comes in, assuming MS was unable to setup a side-by-side configuration for the two Access versions, the next best thing is to do what the OP is experiencing, which is the re-registration of the appropriate components.