The key word here is "overlapping". I think the "old" L1 signal was long enough for the direct signal to arrive first, then have the reflected signal arrive while the direct signal was still being received. This would create the "signal blob".

So yes, the direct signal always arrives first, but gets messed up during receiving by the reflected signal. The L5 signal is so short, that the likelihood of reflections overlapping is reduced. Think: so short that the signal starts and finishes during the time it takes a radio wave to propagate 1 meter through air or so.