The fourth band on the resistor in the image they present is bronze. That means that the calculator is using 20% precision resistors, aka E6 resistors. There is no 200ohm E6 resistor, but there are 150ohm and 220ohm resistors. The latter will give you less current than you wanted, but will not exceed it.

And yes, essentially no one uses 20% resistors anymore. Even 10% resistors can be hard to find.

The calculator is using 5% precision resistors, aka E24 resistors, but in such a way that it is impossible to exceed the given current. With a 200ohm 5% resistor it is possible to have a resistance as low as 190ohm which would result in a current of 15.8mA, thereby violating the 15mA constraint.