Several recent studies establish that crude oil and natural gas prices are cointegrated. Yet at times in the past, and very powerfully in the last two years, many voices have noted that the two price series appear to have "decoupled". We explore the apparent contradiction between these two views. We find that recognition of the statistical fact of cointegration needs to be tempered with two additional points. First, there is an enormous amount of unexplained volatility in natural gas prices at short horizons. Hence, any simple formulaic relationship between the prices will leave a large portion of the natural gas price unexplained. Second, the cointegrating relationship does not appear to be stable through time. The prices may be tied, but the relationship can shift dramatically over time. Therefore, although the two price series may be cointegrated, the confidence intervals for both short and long time horizons are large.