It's not to say that these background sources are wrong. But they're getting pretty filtered info...the after-action report which consists of the compiled recollection of the actual operators.
Again, that report may be 100% truth, and it may even contain known unknowns and concerns of the operators. But can the spec ops officer who talked to the reporter be trusted to have summarized that summary correctly?
Let's say Obama was the New Yorker's secret source. No one would argue that he is not an authoritative and extremely important source regarding the OBL killing. But he is just one source, far removed from the action (remember that there was no helmet cam or otherwise-indoor video), with a definite vested interest in having the first detailed examination of the incident looking good for the WH.