I think you were the victim of an optical illusion, the height of fluidcolumn coincides with the height of the cup, the straw being only semitransparent you thought it was the fluidlevel but it probably was the shadow of the edge of the cup or reflection of the watersurface.

I don't think it was capillary action as a quarter inch thick straw is too thick for that to happen with water and the law of comunicating vessels would be in effect.
And since the straw was open to one end it couldn't be the barometric effect of the Torricelli tube, which requires the tube to be closed on the top end.

It could be an optical effect.

In AdamR's drawing, the water level in the straw coincides with the edge of the cup. Perhaps the cup focused or blocked ambient light in a way that made the straw appear full to the rim of the cup. This would also explain why the water appeared to drain only slowly as he slowly pulled the straw out.

edit: ninja'd by Strijkbout!