Thanks for everyone's concern!
Yes, apparently the hose is dangerously worn. The service rep called to let me know that I could take the car home while they waited for the hose, but later when he told the tech that I was going to take it, the tech told him no...and showed him the car is not to be driven. He called me back and is giving me an upgrade on a rental car.
And, yes, I did record the mileage...17,189. Which may explain why it is more worn than most would expect. What can I say? I go for Sunday (and Saturday) drives and burn a tank of gas each time. I love to drive!