Offhand I can think of two uses for deploying the subtle semantic strategy called "equivocation."  The first is to cover up the fact that you're lying about something; the second is to make it look like someone else is lying because of a verbal sleight of hand.  This latter is exactly what "Politifact" did with their now infamous "lie of the year" award.  First the lie of the year (via WashMo):

Republicans muscled a budget through the House of Representatives in April that they said would take an important step toward reducing the federal deficit. Introduced by U.S. Rep. Paul Ryan of Wisconsin, the plan kept Medicare intact for people 55 or older, but dramatically changed the program for everyone else by privatizing it and providing government subsidies.

Democrats pounced. Just four days after the party-line vote, the Democratic Congressional Campaign Committee released a Web ad that said seniors will have to pay $12,500 more for health care “because Republicans voted to end Medicare.” […]

PolitiFact debunked the Medicare charge in nine separate fact-checks rated False or Pants on Fire, most often in attacks leveled against Republican House members.

Now, PolitiFact has chosen the Democrats’ claim as the 2011 Lie of the Year. 

It turns out, on the most reasonable account, the lie of the year is literally true.  The whole thing, of course, hinges on the meaning of "medicare."  This single-payer government insurance program covers everyone over the age of 65.  The Ryan plan, about which the lie of the year has allegedly been made, proposed to end the "single payer" part of that equation by eventual phase out, replacing it with a voucher system for private insurance.  All the while, of course, this program retains the name "medicare."  But it's not "medicare". 

How not?  A fun analogy, from WashMo:

I’ve been trying to think of the best analogy for this. How about this one: imagine someone owns a Ferrari. It’s expensive and drives beautifully, and the owner desperately wants to keep his car intact. Now imagine I took the car away, removed the metallic badge off the trunk that says “Ferrari,” I stuck it on a golf cart, and I handed the owner the keys.

“Where’s my Ferrari?” the owner would ask.

“It’s right here,” I’d respond. “This has four wheels, a steering wheel, and pedals, and it says ‘Ferrari’ right there on the back.”

That's about it.