Michael Goulder took a lot of minority positions in his scholarly career. But his work on the Psalms of Asaph was probably the best received of his attempts to buck the scholarly consensus.
He assumed that what came together in what we know as the five books of the law, Exodus-Deuteronomy, were still separate traditions when the Psalms of Asaph were composed. Therefore, he doesn’t try to make these Psalms fit with the Pentateuch. When Meribah appears in Psalm 81:7, he does not explain it simply by going to Exodus. 17 and Numbers 20. Rather, he thinks Asaph represents a separate and old tradition peculiar to the Joseph tribes who came out of Egypt together and experienced a testing by God at Meribah (The Psalms of Asaph and the Pentateuch: studies in the Psalter, pp. 155-157). This tradition has Meribah where other traditions would have Sinai or Horeb, the mountain of God.
Goulder notes that neither Sinai nor any other mountain gets connected to the Exodus in any of the Asaph psalms. According to Goulder, the Joseph tribes see Meribah as a place where God offered them a covenant, but they rejected it. He thinks Psalm 78, especially v. 41, refers to this. In the Asaph tradition Merebah’s theme is not Israel’s murmering and there is nothing about water from a rock. The “waters of Merihah” simply mean that the place is an oasis. The Joseph tribes came out of Egypt and stayed at an oasis in the Wilderness of Zin. It was there that they were challenged, perhaps by a Kenite priest, to change religions and worship a single God who had no image (Psalm 81:8-10). Many of them balked at the new religion (verse 11). The other northern tradition–the one source critics call E–recalls the same rebellion with its golden-calf story.
Along with the challenge to worship the new God, came a promise, “Open your mouth wide, and I will fill it” (verse 10). Goulder takes this as a literal promise of food for the people in their precarious existence in the wilderness.
I am not convinced by Goulder. He relies too much on arguments from silence. Maybe the Joseph tribes were the only tribes in Egypt. But other tribes were probably represented, because the Pharaohs had brought back POW/slaves from all over Canaan. Maybe Sinai was not part of the Asaph tradition, but a Jerusalem editor could have substituted Zion for an original reference to Sinai in Psalm 50:2, for instance.
Nevertheless, his thesis is very interesting and probably touches on some truth. The golden-calf story and the water-from-the-rock stories must be elaborations of something that actually happened in the wilderness, But there is no reliable method for recovering pure history now.