True and False. Here's why:
If the quote is a question or exclamation of sorts, then the punctuation should indeed go inside the quotation marks. Ex.
She said, "Oh no! I left the evidence in the trunk!"
Ivan asked, "Do you need milk from the store?"
However, if the quote is NOT a question and/or exclamation then the punctuation goes outside of the quotation marks. Ex.
I think she said she was "alone in a crowd"!
Did you just tell me to "go to bed?"