Why do Buddhists believe that the Buddha was enlightened, despite that he claimed it himself?

All the answers to the question about the [living enlightened people](https://buddhism.stackexchange.com/questions/3058/are-there-any-living-enlightened-people/3352) suggest that talking about one's enlightenment is taboo, so if somebody claims to be enlightened, he probably is not. Why doesn't this reasoning apply to the Buddha? After all, he claimed himself to be englightened (for example, in [Dhammacakkappavattana Sutta](http://www.accesstoinsight.org/tipitaka/sn/sn56/sn56.011.harv.html)) .