Taylor Swift Takes Romance with Conor Kennedy to Nashville

But the couple didn't meet her parents as reported – that Internet photo shows her brother at Father's Day, PEOPLE has learned

Photo: Cindy Ord/Getty; Douglas Healey/Polaris

Taylor Swift‘s love story with Conor Kennedy is moving to her home turf.

On Thursday, Swift, 22, and Kennedy, 18, were spotted at Edley s BBQ in Nasvhille, where she posed for pictures with fans.

“They were both very relaxed and casual and for the most part were left alone to enjoy their dinner with a friend,” one fan writes of the couple.

Writes another: “All I know is that she seems so, so happy right now and when Taylor is happy, so am I!”

Another photo posted by a fan shows Swift dining with her parents and a young man with shaggy hair.

Despite widespread reports that this was Conor meeting her parents, the photo actually depicts her brother at a Father’s Day meal in June, Swift’s rep tells PEOPLE.

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