This is such a common issue wonder why can't CIC find a way out for the applicants who are not in their country of application when passport is requested for stamping. May be because the onus of submitting the passport is with the applicants and they simply wash their hands-off the issue. Although you can get medicals done from any DMP the stamping has to be done by the visa office where the application was filed.
This is not a issue for people from most countries. Because most people can send their passport to CIC in another country and get it back. Instead of CIC finding way out of the applicants who are not in their country, perhaps everyone should petition the Indian government to allow for courier of passports. Indian government simply wash their hands-off the issue. Although you can send your passport with someone, even a stranger, one cannot send it my courier, which is probably safer.