The 10th President of the United States, John Tyler, has two grandsons still alive today [1]. And the last witness to Lincoln's assassination appeared on TV [2]. So someone receiving a pension from the Civil War doesn't seem too far fetched.

[1] https://www.snopes.com/fact-check/heir-raising-experience/

[2] https://www.youtube.com/watch?v=1RPoymt3Jx4