The manufacturer's max cog recommendation is quite conserative but it doesn't mean you can violate it at will.

Shimano's road derailleurs are rated at 27T max but the general concensus is a 28T cog always works, a 30T cog usually works, a 32T cog sometimes works and a 34T cog never works. The type and geometry of the frame's derailleur hanger plays a part in what you can get away with too.