The person you're replying to mentioned a Toyota, which I also drive a newer model of. It has two modes: lane assist (which works like you have described) and lane centering (which automatically is enabled when you switch on cruise control). The centering will continuously nudge you towards what it decides is the center of your lane.

It's awful and I've trained myself to automatically long press the button on the steering wheel to disable the entire system every time I get behind the wheel.