It is probably cheaper for him to cash all checks than to get some assistant to only cash checks over a certain amount. I would imagine there is a department of people who do receivables for him. Most likely it caused trouble trying to find the matching invoice.
Often a proverb will have an opposite proverb (though the example you give isn't a proverb). For example “too many chefs spoil the broth” and “many hands make light work”
The ideal amount of help then clearly rests somewhere between "too many" and "many" :)
Though maybe the proverbs are not exactly opposites. One is about the quality of the outcome, the other is the speed in getting there. Perhaps that's the lesson.
"Pound foolish" is not a necessary outcome of "penny wise", in this saying, but "the pounds will take care of themselves" is. Taking care of the pennies works when one is, at worst, "pound neutral". But being "pound foolish" is an additional condition in the saying, which is not accounted for in the "take care of the pennies" saying.