All true. HOWEVER... The PBY crews were very inexperienced. When the invasion forces were sighted, their location was given, but no description of the force composition beyond "Main Body". When the Nagumo Force was sighted, the position was more or less correct, but only two carriers were sighted. When the Tomonaga strike force was on the way to Midway, it was sighted, but the PBY only reported "Many planes, heading Midway". No call letters sent, no location.
Nagumo came to grief because he only launched a phase one search pattern. Had he launched a phase two search pattern (in line with his own cautiousness) that would have meant Japanese search aircraft coming over Task Force 16 and 17 at dawn! No Midway strike. Or else a delay to rearm for anti-shipping strikes. Considering how long it took for the USN carriers to finally get into the air...
No one in the IJN used a two-phased search. Fuchida, who was the first to introduce the concept into the Midway discussion post war, stated that it should have been done, but the concept didn't enter Japanese doctrine until the lessons of both Coral Sea AND Midway had been absorbed. See Shattered Sword pages 107-108 for a rather interesting discussion on this matter.