To be const or not?

The Incredible Const Reference That Isn’t Const

by Jonathan Boccara

From the article:

While working on the NamedType library I came across a situation that left me stunned in bewilderment: a const reference that allows modification of the object it refers to. Without a const_cast. Without a mutable. Without anything up the sleeve.

How can this be? And how to enforce the const in that const reference?