Keep in mind, a major part of his paper was about how the pseudo-patients were admitted after describing extremely limited and mild symptoms. And a major part of the investigation was determining that, at least in one case, this is untrue; Rosenhan claimed to have extremely severe symptoms, including suicidal ideation.
In other words, it now sounds like the hospitals responded reasonably, but Rosenhan's paper claimed something quite different.
Because what else can be done except to say "ok, there are symptoms, now the symptoms went away, huh." If he was honest, it doesn't reflect that badly on the professionals because there's always going to be cases that fit the pattern.
His distortion seems exactly like every pop-sci article today that is written for outrage-clicks. It seems kind of quaint, even though granted it's an influential paper.
Did Roseanhan claim to have a dr-patient relationship with them. Do they just mean alleged-patients or alleged study subjects?
The distinction is that pop-sci articles are just journalism. Most academics take pop-sci journalism in their field with a grain of salt at most, and usually a hard eye-roll.
Real scientific journal/conference articles are held to real standards. Exaggerating or misreporting results in a scientific article is basically malpractice. It's by far the worst (scientific) thing that a scientist can do.
It's to make the point that he didn't recruit actual patients for the study, but (in his telling) perfectly sane people to pretend to be ill.