That's what the NYT would have you believe. They compare US productivity against European productivity, noting that GMOs are rare in the EU but productivity levels are similar. (This is attributed to "European anger at the idea of fooling with nature.") They do note that no health concerns have been convincingly shown: GMOs are as healthy as any other crop variants.
Further, they contend that GMOs haven't curbed insecticide use, and they have increased herbicide use. The latter claim is almost certainly true: some GMO crops are designed to encourage use of herbicides. Why would anyone want to plant those crops? Well, every farmer has to deal with weeds, and think about how nice it would be to just spray chemicals that know to kill every plant except the good ones. That's what this GMO seed is: the plant isn't affected by the herbicide, so farmers can spray with impunity.
Leaving aside the question of what it means to "fool with nature" (for example, is a human artificially putting a seed into the ground "fooling with nature"? How about killing the bugs that eat the plants?), a few shortcomings of this analysis are apparent.
1) I think most advocates of GMOs would contend that GMOs improve "total factor productivity" whether or not they improve yields. In other words, you might not get more grain per acre of land, but you might get more grain per ton of fertilizer applied, or more grain per hour of human time invested. I don't have any numbers off the top of my head, but these are questions the article doesn't address.
2) Herbicide use is bad, but the alternative is watching your soil be carried down the river. While that sounds like a disaster for the environment, consider this: the other way that people fight weeds is by plowing the land, tearing plants up and driving parts of them underground. this has the effect of facilitating soil runoff. I'm as unhappy about chemicals being sprayed on the land as the next person, but I'm also unhappy when I see the Mississippi River Delta expanding every year because of all the soil carried down the river. Losing soil is a real problem, potentially threatening agriculture itself, and applying herbicides slows the rate of soil loss. (Also, saving soil prevents the release of carbon into the atmosphere, slowing climate change.)
3) Take a look at my former professor David Zilberman's ode to Monsanto, describing his very positive view of the company. His research has shown that skepticism of GMOs has cost the world hundreds of billions of dollars in value... as well as millions of people's eyesight lost due to short-sighted (yuk) resistance to Golden Rice, a genetically engineered product designed to get vitamin A to populations who normally don't get enough, and who often lose their eyesight because of it.