The only exception or waiver to the time requirements is if you have to leave due to civil unrest, war or similar adverse conditions. You must demonstrate that you reasonably could have expected to meet the minimum time requirements if the adverse conditions had not occurred. Each year the IRS publishes a list of countries that qualify, and it is typically very few. In 2013 and 2014, the only restricted travel country was Cuba (and there was a special exception for certain civilians working at the Guantanamo Bay naval base).
The bona fide residence test is arguably looser in terms of time requirements- Yes, a full tax year must be encompassed. But the number of days spent in the United States can exceed 35 (365 minus 330) without jeopardizing your status. The physical presence test is more stringent- there are no exceptions for medical issues, funerals, divorce troubles, sick parents or other scenarios- the IRS simply doesn’t want to hear about it, nor make a bunch of ad doc decisions on the physical presence test.
However, the fourth element of the bona fide residence test is the hardest to meet- “You cannot have any future plans of returning to the United States.” See What is the bona fide residence test?