I think the reason the OP said that Dressage is considered the base of all riding is that it's a codified method of teaching balance, obedience and responsiveness.
The word dressage, as we know it , did not have the same meaning back when the European world's master riders were developing riding in a systematic way that could be taught through both direct experience (in the menage) and by studying of texts. Dressage just mean "practice". I dont' think riding was divided into different types. There was just riding, good riding and bad riding. So, the schools and masters were trying to promote good riding.
So, if you want to say that good riding is the basis of all types of riding, then it is not so strange to say that dressage (in the old meaning of the word) IS the basis of all riding styles today.