It depends. I don't fully buy into that statement and I think it regularly leads to problems in prioritizing work that *has to* be done. In particular, work that isn't visible to customers - unless it's not done. Talking about reliability work.
People tend to forget, but reliability is a key feature of any software. A feature means nothing, if it's not working at the times it is needed. There is, however, not so much value in discussing reliability work with customers. It's worth to explore their expectations, but once that's done: what should the conversation add? It still needs to be planned, refined and prioritized.
Of course, as with tech debt, it makes sense to make it part of usual feature work and make it measurable as you suggest later on. But we have to acknowledge the fact that there will be work remaining where this approach doesn't work.
And FWIW: a story that says "Decrease file upload time by 30%" is still a tech story.