It's always welcome when a restaurant sends you a coupon for a free meal or a discounted meal for your birthday. Less a big deal is when a business sends you an institutional birthday card. Unless there is a handwritten note or at least an actual signature, why bother? It just seems like advertising in the form of a greeting card.
Around the time of my last birthday in early June, I received such a card from a firm that handles investments for me. It was worth opening, but hardly worth displaying with other birthday cards. It did not survive long before going into the trash.
Then in late August, on the same day my wife received her birthday greeting from the same company, I received a second birthday card. It drew a laugh, nothing more.
A few days ago I received a third card, not from the investment company but from the company that sends out those birthday cards for the investment company. This card, with "Sincerest Apologies" on the front, apologized for sending the birthday card that "was sent entirely too early." So they know they made a mistake, even if they are not clear what the mistake was.
The first card from this company was a trifle. The second one was silly. The third seemed somehow offensive. Perhaps the offense, if there was one, lay in destroying whatever illusion may have existed that the birthday greetings, even the erroneous one, were somehow personal, perhaps even sincere.
In a civilized world, we need our illusions. A "good morning" said to a stranger may be somewhat fraudulent but such things can nevertheless make our days a trifle brighter. If we were to say "good morning," then apologize by saying, "I'm sorry, I thought you were someone else," it would break the spell. It would also be rude in its own right.
Not every error requires an apology.