Mowers are not the same quality as car engines or even a motorcycle for that matter .
They are the cheapest engine it is possible to make
Because OHV systems tend to increase the valve lash with use you set them on the tight end of the spec so they remain in spec for longer.
The often you adjust them the better
Side valve engines burn the valve seats so the clearance gets smaller over time thus you set them at the loose end of the spec particularly as it is a ardious task on most mower engines .
The only reason to have any valve lash is to account for expansion so when the engine gets hot the valves are not held open .
As for exact measurements don't beat yourself up over it.
I was at a bike show where the CSIRO had a stand as they were on a recruiting drive
The stand had a set of ignition points ( it was a long time ago ) which were connected to a measuring device accurate to within 0.00001"
Any one who set the points to exactly .030" got a prize and you could use their feelers or your own.
By the end of the show not a prize had been awarded and I got a copy of the results which showed no one got to within 0.0005" of exactly 0.030"
They also had a variety of measuring tools there to check the measurement of peoples feeler gauges and again very few .030" gauges were in fact 0.030" from one end to the other