There is a way round the immediate problem (not sure about IE6 - do we still care about IE6? - anyway, we can sort that later through the IE6 conditional stylesheet).
For the moment, if you try each link:
you will see that the first (unspecified 'root') link causes the problem you originally described. The second (page specific) link gives the desired effect.
The way round this would be to rename the 'index.php' to (say) 'home.php', and then have your index.php empty but for a 0 second reirect refresh to 'home.php'.
For instance, I have set this page to redirect to your index.php, so it works as it should.
That may be a good workaround (at least until Ray pops in and points out the obvious).