Definition of Responsibility:
The obligation to carry forward an assigned task to a successful conclusion. With responsibility goes authority to direct and take the necessary action to ensure success.
As a seller, it is a best business practice to ship an item tracked (if not also insured). Unless the buyer specifically states they do not want a trackable shipment, one would assume that the item would be delivered with some form of delivery confirmation. If you had truly shipped the watch/watches with a tracking number of delivery confirmation then the buyer would be able to see if the package is on it's way, where it is, and god forbid, if it is held up or confiscated in customs, then at least there will be some indication of that.
You, however, have shipped several watches out without any form of confirmation. So you are correct, it is your word against theirs. However, since you seem not to give a damn about their situation and fail to see your obligation in this, and don't seem to want to take any sort of responsibility for your part in these transactions, I am reluctant to side with you and believe that the buyers are the ones telling the truth here.
Own your responsibility here, man up, and do something to help these guys out. Stop being so blatantly cold to these guys and be a responsible human being.
Just my $2.00 worth