Growing under live oak trees in the south?

I'm listening to a survival podcast with Paul where he talks about the 14 or so ways that plants get water.  He mentions planting a carrot next to an oak tree and the oak tree bringing up the water that the carrot needs.

Here, in South Carolina, it is generally understood that you can't grow anything under live oaks because they take up all of the nutrients in the area.  Now with permaculture I am to understand that it is the opposite - the tree brings up nutrients that other plants can use.

In theory then, the live oak should be bringing up massive amounts of nutrients and water due to the massive nature of the tree.

I have observed that there is generally nothing growing under any live oaks.
Is this because the right stuff hasn't been planted?
Is it because a live oak is an exception?

What say ya'll?

My experience with the California Live Oak is that it does not let much sunlight under it.  The ground under many of ours was very compacted (a century of nothing growing under them causes the rains to wash away top soil, plus compact what remains).  Our cars were also parked under them in summers for the shade (none of us had A/C).

We did have several, closer to the creek, that had abundant native growth under them.  My sister planted (I only know it by this name) Wandering Jew under one by the house, and within a few years, the WJ took over that part of the yard, and was expanding.

Oak leaves will make your soil more acidic than pine needles will.  That will limit what does well under the mighty oak.  We loved our oaks, and so did the fireplace!

That's the main problem with Live Oaks, they create very dense shade most of the year, so it's difficult for anything to grow under them that isn't shade tolerant.  Most shade tolerant plants seem to prefer more water than is generally available under our oaks here.

I have heard that some kinds of oaks are allelopathic.

My Grandmother used to grow her strawberries under the Live Oak trees.  They got morning sun and then shade the rest of the day.  They stood up well to those hot South Georgia summers where she lived, and were sweet, delicious and huge! 

That's very encouraging, RedCloud!

we grow lots of stuff under oaks. in fact. there are quite a number of plants that NEED that helping shade, and those deep roots bringing water up to the surface.

Can you list out at least some of the things you grow under your oaks, hubert? 

Thanks.