In British English, "casket" means "a case for holding jewels, etc"; in American English, it means "coffin". Shakespeare, of course, used the term in the former sense.
Early in The Merchant of Venice the problem comes up, of choosing which suitor should marry rich orphaned Portia. Her father's will specified that a kind of game show be played out: each suitor is given a chance to pick a golden casket, a silver casket, or a lead casket; whoever picks the right box wins the bride. (The two wrong boxes hold put-downy "sorry!" notes; the right one (in Act 3) holds a "congrats, you chose wisely" note.)
The setup is described in Act 1, scene 2:
Your father was ever virtuous, and holy men at their death have good inspirations. Therefore the lott’ry that he hath devised in these three chests of gold, silver, and lead, whereof who chooses his meaning chooses you, will no doubt never be chosen by any rightly but one who you shall rightly love. But what warmth is there in your affection towards any of these princely suitors that are already come?
and again in Act 2, scene 7
Go, draw aside the curtains and discover
The several caskets to this noble princegrave.
Now make your choice.
PRINCE OF MOROCCO.
The first, of gold, who this inscription bears,
“Who chooseth me shall gain what many men desire.”
The second, silver, which this promise carries,
“Who chooseth me shall get as much as he deserves.”
This third, dull lead, with warning all as blunt,
“Who chooseth me must give and hazard all he hath.”
How shall I know if I do choose the right?
Note that in these passages "casket" andgrave "chest" are used synonymously.
The right box is the lead one, which of course Mr Right figured out, by reverse psychology
The point about the morticians is that they did not know the story. The play is not offensive to their trade, and they are too ignorant to know this.
Willis's development of the character of the MI is the opposite of nuanced. It supports the conclusion that the MI's objection is founded on ignorance, but anything beyond that seems to me silly.
An exercise of contorted illogic might let one guess that if Shakespeare had written about coffins and not jewel boxes (as he didn't), then Willis's morticians might have supposed the play advocates the use of lead coffins rather than gold or silver ones, so reducing their profits. But this kind of subjunctive counterfactual is not needed to understand Willis's story.