That is correct, and is precisely what happened with Stokke. Stokke came to the polling place was told that her mail-in ballot had already been received. She was given the choice to sign an affadavit claiming that she had not voted by mail, which would allow her to vote in person. She refused to sign the affadavit and then began to peddle her story as evidence of fraud. Really makes you think...
I think in most cases, your in-person vote in that situation is provisional -- meaning it will only count if your mail-in vote doesn't arrive
Jill Stokke was explicitly given the option to have her mail-in vote invalidated so she could vote in person. That was in Nevada; Procedures elsewhere may be different.
This is state dependent. In some states, voting in person after sending a mail in ballot is a felony.