In short: the lack of a direct correlation doesn't seem to phase those in the media from perpetrating the myth. The US economy is too complex an entity to expect one commodity to drive most business activity in a predictable direction.
The price of crude oil as of January 31 close stands at; WTI $51.56/bbl ( 35.1% YTD) and Brent $56.62/bbl ( 14.2% YTD). As one can see from the data for the last five years, the correlation that once existed between the price of oil and its effect on equities, no longer exists. The primary reasons for this decoupling are two-fold. One, the monetary policies in place over that time period (manipulated money supplies and artificially low interest rates) and two, world-wide production capacities are currently at their peaks with no change in demand. Over the next decade, we see the price of crude much lower than present day levels. It will not be a linear degradation, but it will be the trend (from the upper left to the lower right).
Global Oil Production by Country (bbl/day)