The USN narrative is very obviously based on incomplete information, agreed, but it gives good insight into what the US commanders were doing and thinking. That the Japanese had no submaries at the Battle of the Java Sea is now well known, but that the Allied commanders thought there were Japanese submarines in the area could help explain a few things -- why Doorman turned away, why the Witte de With had a depth charge detonate under her stern, why the Jupiter thought she had been torpedoed in very shallow water. There are a lot of unanswered questions about the Battle of the Java Sea that need some examination.
I do not believe anyone questions Doorman's courage and determination. The general consensus that I get from what I have read is that the US and British did not have complete confidence in Doorman's tactical ability. Both Hart and Glassford were not happy with him. Winslow in particular is very, very hard on Doorman, and he has taken hits from Morison ("cautious") and Prados ("reckless"), among others. I don't know how else to take Eccles' comment than as a critique of Doorman, this time for poor communication, which is understandable but does not tell the whole story.
I think many of these criticisms are unfair, given the situation Doorman was in. Some of it might come from national pride ("We could have done better"). Some might come from Doorman's personality; I get the impression that he was not a "people person" blessed with great social skills. But some might also come from the Dutch naval philosophy. The Dutch seemed to prefer leading destroyers into battle; hence the description of the Tromp as a "destroyer leader" and Doorman's otherwise unfathomable plan at Badoeng Strait. The Japanese had a similar philosophy, but the US and the British did not share it. Read in that light, it is not a stretch to read Doorman's (attempted) deployment at the Jave Sea as an adjustment.
What I have yet to see anywhere is an acknowledgment that Doorman cared very much about the men under his command. Yet that is precisely the biggest impression I get of him. Doorman did not want to put his men in harm's way with no potential benefit, with no way of striking back. That was why he withdrew on 2/4 and 2/14. He did not want his men worked to death for no benefit, which is why he even defied orders from Helfrich and withdrew just before the Battle of the Java Sea. When he saw a chance to finally strike the enemy at the Battle of the Java Sea, he took it and did everything he could to make the most of it. That he ultimately failed is of no discredit to him, given the odds he was facing, particularly since, again, he showed concern for his men by ordeing Houston and Perth to withdraw rather than rescue him.