Are you sure you’re not getting your measurements wrong? In my experience most table saw blades are 1/8". 1/4" is pretty thick for a blade that isn’t a dado stack. They make blades even thinner than 1/8" that are perfectly safe as long as they’re used within their rated rpms.
I’ve routed grooves before on a handful of projects. A router with a template will make things easier if you have many grooves. If its only a few, a table saw is fine. The problem with the table saw is the time it will take to adjust the fence for each new cut.
Adding a description or summary of the video would be nice.