"Remember that you have to buy vegetables."
Translation:Pamiętaj, że musicie kupić warzywa.
I don't know if it should be a suggested answer, although maybe it's good that it is, and it's really good that you asked this question.
Actually the situation is quite easy to imagine: you and your brother are about to go to the supermarket, and while your brother is in the bathroom, your mom reminds you to buy vegetables. She says it only to you, but you will be shopping together with your brother.
I can imagine it also going the other way round, although it's less probable: "Pamiętajcie, że musisz kupić warzywa". A friend visits you, you are going shopping together. Your mom speaks to you both, that you have to remember about the vegetables. Only you will buy them, because your friend doesn't live with you, so he doesn't really care about your vegetables, he won't use his money to buy them. But he can remind you about them while in the shop, so your mom tells you both to remember.
Now that you mention it, it does make a lot of sense that the verbs can refer to different people given that they're somewhat independent clauses, my mind just got stuck on the idea that it was ungrammatical instead of thinking about the ambiguity inherent in the English sentence.
As always, thank you to all of the mods for being so quick with helpful responses.