Further on Nadab and Abihu . . . the seemingly endless details in Leviticus 9 and 10 can be read contextually as support for the utter importance of doing “God” things with great intentionality and care.
Lev. 15:1 gives us another clue: “The LORD spoke to Moses after the death of the two sons of Aaron who died when they approached the LORD” [emph. mine, bc], and then God gives a pronouncement to Moses (for relaying to Aaron) relative to careful, intentional, anything-but-haphazard approaches to His presence.
Num. 3:4, like Lev. 15, doesn’t seem to me to draw a conclusion on the exact cause of death. The text, in my view, isn’t acting as coroner here but is emphasizing that a careless attitude toward Yahweh just won’t do. All we have is a connection between the occasion (“when they approached the Lord” or “when they made an offering”) and the deaths.
Also, please note in Lev. 10:9ff the other references to treating with care the Lord’s HOLY presence.
I realize that some of this is conjecture, but the texts don’t state specifically that “the reason God killed them was that He had said to use Fire A, and they used Fire B, thereby committing an infraction of Rule 443.” There just seems to be more to this whole incident than an emphasis on rule-keeping.
Nadab and Abihu trivialized the worship of the Almighty, while the healed leper, Mary Magdalene, and others offered purposeful, spontaneous outpourings and love and adoration. May we, like the latter group, always approach God intentionally and with ardent passion for Who He is—the glorious Lord, on the throne.