Just because a President is in office does not mean his party is "In Power". Besides the President cannot spend tax payer dollars, only Congress has the purse strings, so blaming a president for all economic woes isn't helping much. I realize they are easy targets though.
It's really not that simple.
Black friday, in october of 1987 (towards the end of the Reagan years), the U.S. saw a huge stock market crash. George H.W. Bush took office in 1989 and wasn't really concerned with the weakness of the economy... For a while that seemed like a good idea, as consumer spending picked up in 1990 and it seemed for a bit that there would be no further ill effects on the economy. SO, he spent his time trying to balance to budget - after all, his fellow conservative had Reagan tripled the deficit from 1980-1988 - he cut spending and - in a comprimise - was forced to concede tax increases to the democratic congress. This broke a campaign promise (but that's not really important here)... Economic problems re-emerged in 1990.
So maybe George H.W. Bush didn't cause the 1991 recession but history shows that he definitely failed to solve the problem. Although later(during the Clinton years), the technology boom came and largely erased all of the issues with the economy from this time frame.
The 2001 recession was caused by Alan Greenspan's fed in a pointless battle against inflation (inflation was very low throughout the 90's all the way until present) the fed rose interest rates. As I've pointed out in other threads(maybe even this thread), Greenspan was Reagan's guy. On a related - and also previously mentioned note - Greenspan's actions during this time have been pointed to as a key cause of the 08 recession.
So, while it is true that the president isn't always to blame... George H.W. Bush only showed incompetence dealing with his economic crisis and Alan Greenspan - following conservative economic principles - essentially caused the 2001 and 2008 recessions. Therefore, my assertion that those recessions happened with Republicans in power is correct.
Allow me to point out that in that very same statement you quoted I said the 1981 recession wasn't Reagan's fault and as I've said before it was Fed chairman Volcker who created the recession of that time (he also is responsible for the recovery)... The difference between Volcker's war on inflation and Greenspan's was Volcker got a 10%+ core inflation measurement down to ~4%. By the time Greenspan decided to embark on his own war on inflation - inflation wasn't even a big problem - it was as low as 2%.