Full flow staged combustion engines like Starships do not have significant un-burnt methane. They run slightly fuel-rich, but that results in extra CO emissions rather than CH4 due to the temperatures involve -- methane cracks at 1200C, Starship engine temperature is 3000C.
Starship's operations in Boca Chica do emit methane during ground operations. The mitigation for that is to use a pipeline rather than trucks for delivery.
Solid rocket motors emit all sorts of nasty stuff, like aluminum particles.
I think what they were trying to get at is GHG emissions in general which there are more of than just CO2.