I think the argument is: It’s normal to the direction of travel, so it does increase velocity, and eccentricity is what you get when you add velocity at one poi

I think the argument is: It’s normal to the direction of travel, so it does increase velocity, and eccentricity is what you get when you add velocity at one point in an orbit. Same as other burns. If you were to burn retrograde of normal (but still tangent to the orbit’s radius), there’s an orientation where the retrograde component of your thrust matches the component in the component that’s...prograde in a new orbit. Which now sounds to me like it would just be 45° from retrograde, tangent to the radius