Plants competing with algae

I think all of us at one time or another have stated that it's good to
densely plant because "plants outcompete algae for nutrients".

I've always felt uncomfortable about this.  Does anybody know the
basis of this statement?  Can plants use nutrients faster, thus
removing them from the water before algae can use them?  This seems a
little far fetched.  Nutrients should be evenly distributed in the
water column, easily usable by anything nearby.  

I prefer the "allelochemcal" reasoning for dense planting.

Any opinions?