More Media Ignorance of Simple Economics: Is cutting payments to doctors the same as cutting benefits to those receiving services?

One would think that even the media would understand that cutting payments is the same as reducing the quality of service.  But take this from the left wing Politifact (8/29/12):

In fact, the law limits payments to health care providers and insurers to try to reduce the rapid growth of future Medicare spending. Lawmakers said they hoped the measures would improve care and efficiency. Those savings, spread out over the next 10 years, are then used to offset costs created by the law (especially coverage for the uninsured) so that the overall law doesn't add to the deficit. Ryan's statement is exaggerated and we rate it Mostly False. . . .

Or take the Washington Post (8/15/12):

The Medicare Advantage cut gets the most attention, but it only accounts for about a third of the Affordable Care Act's spending reduction. Another big chunk comes from the hospitals. The health law changed how Medicare calculates what they get reimbursed for various services, slightly lowering their rates over time. Hospitals agreed to these cuts because they knew, at the same time, they would likely see an influx of paying patients with the Affordable Care Act's insurance expansion.
The rest of the Affordable Care Act's Medicare cuts are a lot smaller. Reductions to Medicare's Disproportionate Share Payments -- extra funds doled out the hospitals that see more uninsured patients -- account for 5 percent in savings. Lower payments to home health providers make up another 8.8 percent. About a dozen cuts of this magnitude make up the green section above.
It's worth noting that there's one area these cuts don't touch: Medicare benefits. The Affordable Care Act rolls back payment rates for hospitals and insurers. It does not, however, change the basket of benefits that patients have access to. . . .

Similar comments are provided by The New Republic via NPR under the headline: "Who's Raiding Medicare? Not Obama."

You paid in to Medicare for years. Every paycheck. Now, when you need it, Obama has cut $716 billion from Medicare. Why? To pay for Obamacare. So now the money you paid for your guaranteed health care is going to a massive new government program that's not for you. The Romney-Ryan plan protects Medicare benefits for today's seniors and strengthens the plan for the next generation.
It's not very subtle. And it's not very true. . . .

Yet, the funniest comments come from FactCheck.org, which points out that Obamacare "Stipulates That Guaranteed Medicare Benefits Won't Be Reduced."  So you cut payments to providers, but mandate that they keep providing the same level of service.  Well, that solves the problem for sure.  Why not eliminate payments and mandate that services remain unchanged?  The whole thing is just absurd.