Don't worry, this will be not as pedantic and far less insolent than it sounds. But why not take an objective, definitely (definitely! I sarcastically point out) categorical look at Poltergeist? It doesn't happen too often. (Didn't say I wouldn't be a little bit smug.)
Outside of holding thoughts that the "Spielberg family" quality is not exactly E.T.-pitch preciousness here, really now, or that Poltergeist is in fact far too molasses-like to be an Amblin film, kind of just look, you know... outside of that, I hold no doubts Spielberg posed a major creative hand in the picture. Meaning to be completely and entirely discriminate in this post on how I treat facts, operating along that thin shield across from which lie what we can and what we can ever know, I do not, repeat, do not, know that any accounts I purport here to be reliable are in fact reliable, or that my deductions from these accounts are in fact correctly reasoned.
I do not know... but I can reason, from that one account of things, that the ruckus over directorial duty was instigated by a day in which the Los Angeles Times arrived for a set visit, leading to their subsequent reportage expressing confusion having witnessed Spielberg doing his powerful-producer thing over in the front of the house - shooting Second Unit the Suburban Schlub biking the six-pack over to catch the game - while Hooper was in the back, shooting Robbie in the tree and the canary funeral. Overlooking the strange notion that the LA Times would overlook going to the backyard to see Hooper and the majority of the cast, then we can conceivably take the canary funeral and, through the principle of divided duty, attribute it to Hooper at least partially.
Now I do not wish to push Spielberg out of the picture (well, I can wish, but must I be so petty, is the question...), and clearly there is the evidence of the numerous production photos of Spielberg director-pointing (and his near-constant presence), and so this little anecdote, of a day of seemingly clearly defined duties and delineated whereabouts, must be taken as a simple novel gift, existing in a situation in which it does not need to exist, for the film exists just fine as a work of a clearly vigorous, alchemical collaboration.
Again, not that all things are cleanly made distinct now. Not that all decisions are made on the shoot day, but some decisions are made on the shoot day. Most, I'd say (from experience). But who knows about a production as big and surely organized to the last detail as Poltergeist's? Who knows about a lot of things? Yet this particular moment from Tweety bird's funeral rings with a sort of simple, deferential meagerness, an ornate but modest moment of hairsplitting triviality (it's the scene where the girl buries the bird, what's to discuss?) that rings of having been conceptualized - "directed" - on-the-fly, conceived only while staring at the actors' first rehearsal, not having been subject to the deadening effect of meticulous storyboards (those things Hooper hates): a moment of two simple tilt-ups used as punctuations, plus an impressing shot of a mother's hand submerging the childhood artifact in earth and an unnecessary one of the dog.
Then the casually gawking, modernly irreligious older daughter is pulled down and made to kneel in the old tradition, cuing the cut to the wide shot and the backwards track of the camera along the path of the hallowed mound, lined with flowers.
("Now I lay me down to sleep...")
The camera move, unfortunately, is slightly imperceptible in the screen caps. But the Hooperian structure is all but apparent, another mathematical scene - consisting of 4 camera set-ups - in which two skeptical, secular tilts upward are the arithmetic needed to add to the scene's hallowed, venerated capitulation of a wide shot, in which all players now kneel for an at-this-point unknowing story about modern players' relationship with the dead: an image laced of an ironic religiousness as it witnesses age-old, atavistic funerary tradition accommodated to the simultaneously materially false, yet emotionally and immediately sincere (the mother really loves her daughter, the mother really, herself, planted those somewhat-illustrious natural flowers, which is innately some [atavist] rebellion against the commercial suburb in which aestheticism and naturalness is actually the least concern) modern world of the suburban bubble and the pertinaciously unbroken family.
And this concludes what is perhaps the only objective case we have on Poltergeist, and even then it's not.