This was my thought as well. I've seen this with UP fares as well, where the agent tells me I'm booked in a lower class.

No idea what the formal policy is, but when I purchase the fare it's called a first class fare throughout the process. It seems there needs to be some agent training on these fares. This is not a CPU. At the end of the day, if it's H, fine. But 99.9% of people don't understand this and it causes a lot of unnecessary frustration in the type of scenario described here.