At some point in time other liquids besides oil began being added to crude oil output by the reporting agencies. These are primarily natural gas liquids, and can also be ethanol and maybe a few other liquified gases. Surprisingly, they also include the amount that input volumes increase during refinery processing, known as refinery processing gains.
If you are being technically correct, when giving a production figure that includes crude oil and other liquids besides crude oil, you say - "total liquids" or "liquids" or "petroleum and other liquids" - production. But it is often the case that the term "oil production" is used instead, to refer to a combination of both crude oil and other liquids that are partially substitutable for crude oil. However, I have never seen natural gas liquids added to crude oil and the result referred to as "crude oil" the way the quote in your question does:
Total crude oil production in the US, including liquids separated from natural gas
This April, the US had a total liquids production of 11.27 million barrels per day, of which 8.3 million barrels a day was crude oil. So April's figure would have included 2.97 million barrels a day of output that was not crude oil.
I don't have any figures for how much natural gas liquids Saudi Arabia produces. However, it can be estimated as they are a byproduct of natural gas processing. In 2012, Saudi Arabia produced, 3,258.16 billion cubic feet of natural gas. In the same year, the United States produced 25,307.949 billion cubic feet of natural gas, or 7.7 times what Saudi Arabia did. So Saudi Arabia should be producing less than a seventh of what the US does - which using April's US figure of 2.97 million barrels a day or "other liquids" (which is not entirely NGLs), would mean they are doing less than .424 million barrels a day.
This June 15th, 2014 article talking about US "total liquids" hitting an all time high, also mentions Saudi Arabian crude oil production as being 9.7 million barrels per day.
So the United States has a higher "total liquids production" than Saudi Arabia. But, if we take 9.7 million barrels a day as the Saudi Arabian crude oil production, and 8.3 million barrels a day for US crude oil production, Saudi Arabia still has higher "crude oil production".
So the answer is yes, if you are talking about total liquids production and no, if you are talking about crude oil production.
However, US crude oil production is predicted to increase through 2019 by the EIA, so it is still possible that the US will surpass Saudi Arabia in annual crude oil production in the future.