It's a story so tidy, one almost doesn't want the British tabloid to bother fact-checking it. The paper's initial (and thus far only) source is a "top media lawyer" named Mark Stephens. Presumably, then, the anecdote will be confirmed as the case winds its way through the British courts.
It's worth noting that the Sun doesn't yet know so much as the name of the husband, much less posess the "Street View" image in question.
But there have been enough examples of unexpected and embarrassing Street View pictures that he point of the story stands regardless of whether it's fact or fiction: Google is happy to provide you with enough privacy — say, via GMail and GChat — to get yourself involved in some illicit scandal. Then it will happily bust you as that scandal unfolds in the real world.
UPDATE: Stephens mentioned this divorce case in a sly piece he wrote for the Times of London poking (it would seem) a bit of fun at the hubub over privacy as it related to Google Street View. After tracking the media lawyer down (via email, alas, not Google Street View) for a chat, we're confident the Sun is relaying his story correctly (in broad terms at least). We're confused, though, as to why a random blogger, "Idiot Forever," is claiming to have "duped" the Sun when he or she is clearly not the source of the paper's story. Maybe "Idiot Forever" was trying to put one over — on us. Shrug.