My family and I have purchased new Rollies from ADs in Europe, HK, Macau, UAE and M'sia; and in all instances, it was all hand-written dated. Point to note was that I almost always found that Rollies' post-discount prices were more competitive at the above overseas ADs compared to locally. I have sent a piece or two of these to Rolex SC M'sia for time-checking and recalibration, and no issues with warranty claims at all. Unlike other Swiss and Japanese brands that I have purchased where the ADs were willing to leave the date on the warranty card blank for filling-in only when there was such a requirement, Rolex ADs have never accommodated to such a request as I was told that it was a specific instruction from Rolex HQ and also to prevent re-sale as new units by grey resellers.
The only Rolex warranty card that I have that was stamped/printed, was for Rollies sent in for overhaul-servicing at Rolex SC M'sia. An additional 2-year warranty card was issued, with the date of collection and country unprinted on the card. Hope this piece of info helps.