you are right, richemont sg charges for verifcation. depends on brands also ranging from SG$80 (for pam) up to SG$105 for vacheron (inc gst).
of cos they will give u a nice pouch and cleaning cloth and call it a simple service, and a verification receipt which can be used if u resell it.
rolex service center charges SG$75 which also includes a pouch and cloth but NO RECEIPT or PAPER at all.
AP on the other hand is best, they will do everything and even give you a AP pouch all for F O C.
if u ask them to do a water resistance check, it's free and for some watches even extends your warranty for another year (for new watches under 2 years old).