The article said he was doing some sort of rowing exercise, which would imply he was sitting in some fashion. The article doesn't say, but I suspect he was sitting on a chair or stool. It would be hard to fall when your rear end is on the floor.
A little more information on the case. From the article:
“Worse still, it seems Reid threw the band out after the incident, meaning that no one involved in the lawsuit has the exact item Reid was using, and it’s not immediately clear that the product was an actual TheraBand manufactured or sold by Hygenic.”
https://www.dailywire.com/news/45267/harry-reid-suing-makers-theraband-over-his-eye-emily-zanotti