The story you're about to hear is true. The names have been changed to protect the innocent, at their surprisingly adamant insistence.
So the other day I was talking to a co-worker, Micole Arny, about the fact that she had come back from lunch very sleepy and somewhat confused, at which point she uttered the following phrase:
"Do you know what's fault it is?"
She was going to follow this up with a description of the enormous burrito she had just consumed, but was immediately interrupted by my impassioned demands to know whether she had just said what it sounded like she had just said.
It's confirmed: not only did she say this, but she felt completely unselfconscious about it even when questioned. Clearly this is an exciting development.
That this could happen is, of course, not all that surprising, especially by analogy with "whose" which sounds like "who" plus a possessive suffix (in fact, isn't "whose" hwæs in OE, the genitive of hwa "who?" This makes sense because hwæs would also be the genitive of hwæt "what," giving rise to this whole problem). It is, indeed, a fairly stupid thing about English that it lacks a standard way to relativize an inanimate possessor in a manner that doesn't sound completely ridiculous: "the book whose cover had been defaced" sounds marginally acceptable, but certainly not "Do you know whose fault it is?" with the meaning that Micole intended.
...and so we're forced to circumlocute, or if we're more adventurous, invent some new, more convenient morphology. Any bets on whether this one will be "normal" in 100 years?