"c. If a play-off of any type is not feasible, matching score
cards is recommended. The method of matching cards
should be announced in advance and should also provide
what will happen if this procedure does not produce a
winner. An acceptable method of matching the cards is
to determine the winner on the basis of the best score
for the last nine holes. If the tying players have the same
score for the last nine, determine the winner on the
basis of the last six holes, last three holes and finally the
18th hole. If this method is used in a competition with a
multiple tee start, it is recommended that the “last nine
holes, last six holes, etc.” is considered to be holes 10-18,
13-18, etc."
Sean et. al.
The USGA recommended method is the same is the R&A, as noted above from the USGA website. They do recommend a playoff, but this is hardly feasible in a club stoke play competition where competitors come and go during the day and the results are not known until the last player posts his or her score.
It's a slightly quirky method, but not deserving of your wrath, IMO. Can we assume that you lost a countback on a monthly medal at some time in your past?
Cheers
Rich