"Feedbacks in response to climate variations during the period 2000-2010 have been calculated using reanalysis meteorological fields and top-of-atmosphere flux measurements. Over this period, the climate was stabilized by a strongly negative temperature feedback"
http://journals.ametsoc.org/doi/abs/10.1175/JCLI-D-11-00640.1?af=R There might be room for differences about how the stabilisation was achieved but not as regards the stabilisation itself.
If one says that the stabilisation was achieved by La Ninas then it follows that the earlier warming was caused by El Ninos.
That begs the question as to why the late 20th century El Ninos were so strong.
The best explanation is reduced global cloudiness caused by more zonal jets allowing more sunlight into the oceans.
The problem for AGW theory is that the positive water vapour feedback is supposed to result in more clouds but that didn't happen.