That's a very true, and simplistic statement.
Finches eat a lot more than seeds.
A seed only diet will usually result in an unhealthy finch in the long run. You see wild birds visit your back yard feeders and happily take the free seed feast you have laid out, and most people will agree that wild birds eat more than seeds alone. They can be seen picking around in the ground looking for little bugs, or in bushes and trees looking for berries or sap. Over all a wild finch has a varied and complete diet. What many people don't seem to grasp is that little finch in your living room aviary is also a wild finch.