The paint on the nightgown turns out to be a vital clue to the mystery of the Moonstone theft. It is initially assumed to belong to Rosanna, but turns out to belong to Franklin, who has no memory of changing it, or being involved with the theft in any way. When he is trying to come up with explanations, he asks Betteredge if he had been drunk, or walked in his sleep, during that night. Betteredge responds first that he himself had watered down the alcohol, so that Franklin could not have been drunk, and also that Franklin has never walked in his sleep. Furthermore:
"The Diamond has been taken to London, since that time. The Diamond has been pledged to Mr. Luker, since that time. Did you do those two things, without knowing it, too? Were you drunk when I saw you off in the pony-chaise on that Saturday evening? And did you walk in your sleep to Mr. Luker's...?"
(Collins, The Moonstone, gutenberg.org)
In other words, even if one or both of those explanations were correct, they would only account for the theft and not for the subsequent movement of the Moonstone. Betteredge correctly assumes that someone outside of the household has been working with the Moonstone, for an unknown purpose; neither solution explains the intervening time, during which the Moonstone has been out of Franklin's reach. Interestingly, the real solution turns out to be a variant on both explanations, and is discovered only near the end.