Yes, I think it's an incorrect statement by someone being confused between hardness (scratch resistance) and toughness (resistance to fracture). Diamonds are the hardest naturally occurring material known, yet as far as toughness is concerned, it's pretty mediocre. Aluminum is "tougher" than diamond. Saying that Graphene is as "tough" as diamond isn't doing it justice. Diamonds can cut through everything due to their hardness, yet are easily shattered with a hammer. Most industrial materials are "tougher" than diamond.
Even if you're looking at tensile strength, (how much pressure something can withstand before deformation) diamond isn't the top performer. Diamond's ultimate tensile strength is only around 2,800, which is surpassed by materials such as carbon fiber, (4,137) and even plain old, naturally occurring Silicon (7,000).
Graphene's ultimate tensile strength however, is an astonishing 130,000! The nearest challenger being Carbon Nanotubes, that can reach up to 63,000.
Anyway, yes, having a substance that has such a high tensile strength, and can conduct electricity better than Silver (the most highly conductive metal) is quite exciting, and as the scientists who created it stated, this will indeed change the way we live!
I can foresee huge changes even in just power transmission! No more bulky, copper power lines. (Assuming that the reduction in power transmission loss and repairs due to natural disasters (downed powerlines) can outweigh the production costs)
And obviously, lighter/stronger electronics that have much higher temperature tolerances. Electronics subjected to temperature extremes don't have a long lifespan because of the constant flexing of the circuit traces when heated/cooled. Graphene would stay flexible enough that this would no longer be an issue.