No, the logic is not strange.
Money handed to people in exchange for nothing is worth exactly that. Of course they can spend it, because other people have produced goods and services, which imparts some of the value of those goods and services to the money. In turn, the value of the money is diluted by the amount of money handed out in exchange for nothing.
Maybe it would be easier to understand if I push the description to the limit. Imagine if all people were receiving a guaranteed minimum income, and no one were working. In the absence of goods and services, how much would that money be worth? Could any quantity of money, no matter how large, substitute for the absence of goods and services?
Similar to what the Fed is doing?