Win as if you were used to it,
  lose as if you enjoyed it for a change.

That is, if you're humble enough to put your ego aside.

The business partner sent my client an angry email demanding to know how the mistake could have been made. It's very likely that it was the business partner's mistake, very unlikely that it was my clients mistake... but "oh, hey! our consultant was working near that issue, maybe he touched it?! We'll ask him right away, Mr. Angry Important Business Partner!"

Problem is: there's no possible way to know who did it. Shifting it back to the likely source (business partner's team) will only make him more angry, whether or not they are responsible. As a consultant, I can only loose.

So I write an email to him, CC my client, and apologize for the mistake, promising that it won't happen again. My client knows I didn't do it, and now knows that I willingly took the bullet for him.

Maybe SGaaS is a valid business model, where SG = scapegoat.

Another one of my favourites: Phrasing a request like you're asking a favour even though you're just telling someone to do their job.

One could argue that consultancy firms are already in this business, as you've just described.

When unpleasant decisions need to be made, hire a bunch of consultants who can 'rubber stamp' it so the management and board can pass the blame.

"That would reduce to the halting problem"

Or my favorite,

"If you can solve that problem, there are much more lucrative applications for the technology than [what you're working on]"