FWIW, I remember an equipment review done by Cook's Illustrated or Fine Cooking. They said cookies with high butter contents should not be baked on insulated cookie sheets. Something about the insulation causes the butter to melt prematurely leading to leakage. Using parchment paper on cookie sheets, from what I understand, can work similarly (though not as extremely) to using insulated cookie sheets. Perhaps that is why the woman on the food network said what she did--maybe she didn't mean that parchment paper "draws out" the butter, but that it may cause the butter to melt prematurely and leak out of the cookie.
I actually like butter leakage for certain cookies--like crispy oatmeal cookies. You get a really delicious crispy outer ring of butter and sugar. Yum!
rona