one can use cheap 1% components measure the component's actual value using a good quality DVM and and check if its lying within required tolerance band or not

If you select "precision" from non-precision you are very likely going to miss.
A .1% resistor will/should have a much better temperature coefficient than a 5% resistor. So, you select your resistor from a 5% batch and then heat it 3 degrees and it is not a match any more OOPS. If selecting .1% from 1% you may be able to get by, but you will have to select a match that is sufficiently better than the required to allow for the tempco.

Now for the stick in the wheel: how precise id your ohmmeter?

Erik