I agree with your overall argument. However, the focus of this article has never been the SPR for exactly the reasons you give. In any event, using the SPR would have only a temporary effect.
Rather, President Obama’s only source of real leverage vis-à-vis Russian President Putin lies currently in American “stranded” oil. Given surging US oil production, as shown in the article, the US is in an extraordinary strong position which it needs to take advantage of. But instead of focusing on the US Strategic Petroleum Reserve (SPR) as instrument, President Obama should approach it from the vantage point of the US oil export ban and contemplate an executive order allowing the US to respond quickly to its potential international responsibilities citing national security.
Moreover, just think about what such an announcement by President Obama regarding US oil exports would do to expectations regarding future oil contracts. It will create downward pressure on crude oil prices.