The method I used to use to ensure I has the dipstick level on max after an oil and filter change is as you describe; top up oil using oil filler cap to MAX on dipstick (being sure to allow a couple of minutes for oil to find it's way to the sump). Start the engine and allow it to run for a short time. Switch it off and leave it for a short time, re-dip the sump and add oil to bring the level back to the max marker on the dipstick. This method I've always found perfectly acceptable. I've never seen the oil light stay lit once the engine is started the first time.
That said, I was servicing a car with a spin-on type oil filter with a friend of mine some years ago. My friend works on all kinds of vehicles including military and pre-war. Prior to handing me the filter to refit, he filled it with a small amount of new engine oil. When quizzed on this, he told me that oil is drawn from the sump into the filter prior to being supplied to the engine and filling the filter first means you avoid the few seconds at initial startup when the pump if simply filling the empty filter.
It's important to refit the sump plug prior to attaching an oil filter full of clean oil though. Whilst most genuine oil filters will have a non-return valve, there is scope for a small amount of clean oil to escape during this operation and you don't want that to escape onto the floor.
Also, even with this method you need to start the engine and stop it again to check the true oil level prior to considering the job complete.