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