It's not really a message from the passenger. They updated their ride to include the additional stop (a feature), and are apparently allowed to do this realtime for the trip they are currently taking.

For the driver this would just appear like their current destination suddenly changing, which I guess you have no option to deny except for asking them to leave your car and canceling the trip entirely.

Being able to make major trip changes mid-ride is pretty crappy for the driver. I'm also surprised the multiple stop feature isn't just for simply letting someone in/out of your ride. But apparently Lyft actually encourages you to use it to stop at the store. [0]

Whether you’re picking up a friend or a bottle of vino, just add your stop into the app and your route will instantly update — making it a seamless experience for you and your driver.

The person in the article was driving for Uber. The verbiage on Uber's site for this feature is more focused on passenger pickup/dropoff, but also doesn't make it clear whether you're allowed to spend time visiting a store. I found a rideguru post indicating you're limited to 3 minutes at a stop, but can't find this officially.

[0] https://blog.lyft.com/posts/add-a-stop

[1] https://ride.guru/lounge/p/whats-the-2-stop-rule-on-uber-is-...

Edit, found this on an Uber blog post. Do riders really know, Uber? Do they?

Riders know that each stop should be less than 3 minutes, so you can get back on the road as soon as possible.

https://www.uber.com/blog/multiple-destinations-us/