No. Not referring to Green River. Eagle Ford and Permian (Sprayberry) and horizontal drilling mostly. These are not the articles I originally read, but say the same thing in a dumbed down version.
http://www.breitbart.com/Big-Peace/2014/04/16/American-Oil-Reserves-Now-Top-Saudi-Arabia
http://www.dailymail.co.uk/news/article-2463148/U-S-overtakeS-Saudi-Arabia-worlds-biggest-oil-producer-jump-output-shale.html
http://pbpa.info/education-center/oil-and-gas-101/drilling-and-leasing/spraberry-formation/
So the first link makes your claim, but only if out reserves are 10 times greater than reported with no basis for the claim.
The second talks about production not reserves. There we are greater producers of oil only if you pretend condensate, natural gas liquids and biofuels are oil.
The third talks about a large amount in a single field that mostly uneconomical to produce, that amount is not reserves. Oil in place that cost more to produce than it is worth is not counted as reserves.