Do HTML5 browsers have to be able to properly process HTML4 tags when the tags appear in HTML5 pages?

According to the post here, the HTML5 specification requires HTML5 browsers to be able to properly process HTML4 tags when they are in HTML5 pages.

Unfortunately, the post doesn’t very well substantiate this claim. Can someone answer this StackExchange question, and if the answer is ‘yes’, can they also please substantiate their claim with reference to specific sections of the HTML5 specification in a precise way?