If PO/Thirst/Gifts decks start rising up, the Mentor/Shops decks will just pack more Stony Silence/Null Rod and other cards like that, and they'll drop back down again, much like more Dredge leads to more GY hate.
First of all, PO and TfK are pretty awful cards. They definitely aren't deserving of being lumped into with Gifts Ungiven. Second, Stony Silence doesn't do enough on its own. I only play 7 artifact mana sources.
You ignored the other part of the sentence, which said "and other cards like that."
Specifically, in the case of combating Gifts decks, Grafdigger's Cage is a custom made hoser.
It's the single best anti-Gifts card ever printed, possibly. Since it stops Recoup effects like Snapcaster/JVP, and Tinker/Will simultaneously. If Gifts starts doing very well, you're going to be facing Cage much more often.
Thanks for the response, Steve!
Grafdiggers is good at shutting down Tinker and flashback effects, true, but it doesn't shut down Gifts Ungiven or Baral Chief of Compliance. The flashback effects bring about quick and easy wins, though it's still possible to navigate to lethal without the graveyard and to use Gifts Ungiven as a spell that grants free spells, mana, card draw, or counterspells.
What deck would play Grafdiffer's Cage?
Obviously it doesn't help Shops or Outcome since I bring in more than enough artifact hate already. So you must be talking about Mentor. By bringing in Cage, you're turning off your flashback spells as well; Mentor usually plays only 1 less flashback spell than most of the Gifts list I've played, so that's basically an even exchange; we're both hurt equally, maybe the Gifts deck a little more depending on the hands. The other thing to consider is that Gifts is siding out Tinker\BSC against a Dack/Plow deck. In its place I had been playing Subterranean Tremors but have recently switched to Empty the Warrens. In combination with the other cards that I bring in against Mentor (Leovold, Necropotence), there's a chance that Cage is meaningless.
One more aspect to Gifts that helps its immunity to any single "hate card", is that it is a control deck first, combo deck second. The tutoring power of Gifts Ungiven allows you to devote a very small portion of the deck to actually combo pieces, since you can bring them all up at once with just one card (Gifts Ungiven). This allows for more cards that interact with the opponent and less dead draws to make advantages as you're jockeying for position to cast a Gifts and win. Mental Misstep, Force of Will, Mana Drain, and cards like that make up the Gifts decks frontline defense.
Last but not least, this deck isn't dredge. It's flexible and attacks from more than one angle. If more Mentor players start bringing in Cage against me, I can adjust my sideboard plan accordingly and either take advantage of their tactic or counter it.