Validating a method to meet accuracy criteria using precision and accuracy?
Possibly, but the rational is a bit convoluted. 

First, as you noted there is a fundamental difference between precision and accuracy. You explained the difference correctly.

Now let's think of a hypothetical example. Suppose that you have a pan balance in the lab and an analytical balance down the hall in a balance room. 
So you are going to use the analytical balance (which is accurate and precise) to validate the pan balance. 

You weigh a rock specimen on the pan balance and the weights have a precision of 10%. This means +/- 10%. So to get a better precision, you weigh the rock multiple times. Now the average weight will have a better precision than a single weighing. The average will be smaller by a factor of 1/sqrt(n). So 4 weighings will give you +/- 5%.

So you get a bunch of rocks that span whatever weight range that you would use. You weigh the rocks on the pan balance and on the analytical balance (which is assume to give the "true" weight). Now you can establish a calibration curve for the pan balance. 

The calibration curve is going to have some error too, so you'll probably have to adjust how many repeat measurements and how many different samples you need to get the desired accuracy. But it should be possible in this example. The real twist here is how you "validate" the calibration.