Source: Michael Fishbane's Biblical Interpretation in Ancient Israel (New York: Oxford, 1988) 327.
"A reflex of [the Exodus 16 manna] tradition is incorporated into a historiographical psalm, Psalm 78, amidst a catena of instances where Israel disregarded the manifest goodness of God towards Israel...While the author of this Psalm may have known the manna and quail tradition of Num. 11 (and possibly even a different sequence of the desert traditions from that found in its received Pentateuchal form), the explicit reference in Ps. 78:24 to the manna raining from heaven, and the description of the manna in Ps. 78:24-5 as a heavenly good, strongly suggest that the composer was in some manner dependent upon the formulation preserved in Exod. 16. An inverted witness to this dependency is the transformation of the original act of divine testing (cf. Exod. 16:4) into one whereby Israel tested and rebelled against YHWH (cf. Ps. 78:18). No testing tradition is referred to in Num. 11."
I don't know. Psalm 78 also refers to God's destruction of Israelites in the context of the manna story. That doesn't appear in Exodus 16, as far as I can see, but it is in Numbers 11. The problem, of course, is what Fishbane cites: Psalm 78 focuses on manna, not quail. Numbers 11 talks about quail, whereas Exodus 16's concern is mainly manna. So which chapter is it interpreting? Perhaps Psalm 78 is conflating details from Exodus 16 with those in Numbers 11, as if he's concerned with God's actions, not necessarily the order in which God did them.
Or could Psalm 78 be referring to a story that circulated in the culture rather than specific texts? Fishbane denies that every prophetic reference to Sodom and Gomorrah has to have Genesis 18-19 in mind. So why does Psalm 78's reference to manna have to be an interpretation of Exodus 16?
If Psalm 78 conflates a variety of traditions, why must we assume that it's reversing Exodus 16's story about testing, making it Israel testing God rather than God testing Israel? There are stories in the Pentateuch in which Israel tests God (see Exodus 17:7; Numbers 14:22; Deuteronomy 6:16; 33:8). Rather than reversing an Exodus 16 theme, maybe Psalm 78 is saying that Israel also tested God by asking for food.