Someone correct me if I am wrong but:
If they are already requesting the passport to stamp it and make it ready for landing in Canada, then he should not have to renew his medical exams as he has already been accepted into Canada.
Well, the difficulty of the situation described is that according to Canada's IRPA the immigrant visa is valid for 12 months from the day of the chest X-ray... I.e. with the current medical exams on file, the visa expiry date would be Jan 25 2012, which doesn't leave much time for the person to probably even buy air tickets not mentioning sell lifetime possessions, arrange a place to stay etc. in Canada, pack and fly...
If the applicant had his medicals re-done in December 2011, they should inform the embassy about it and get a confirmation from them that that they will put issuing immigrant visa on hold till the new medicals have been received and processed... I.e. the new visa will be valid till December 2012...
Otherwise, speeding up getting the visa in passport and leaving your home country all within two weeks, even though possibly an option but hardly a wise one... But the applicant is the one to decide.