Saying we are incorrect doesn't make us incorrect. The Dwemer share many similarties with common dwarves in literature/games/whatever.
The Dwemer were masters of crafting and smith-work. They even created an Aetherium Forge, a highly advanced smithing forge to... you guessed it, forge weapons and armor! The Dwemer mainly focused on metallurgy, the study of the physical and chemical elements of metal, just like Dwarves. Because of this, they were able to create their own distinctive form of metal which was easily mistaken for bronze.. bronze being a common Dwarf motif as well. And yes, many Dwemer did in fact live underground. Not all of them, however.
Also, from this concept art... it looks pretty evident that they were intially based on dwarves. There is nothing to compare them to in this picture, but they look anatomically shorter than average & have beards. They are also pictured with weapons and shields that they presumably made themselves.
Morrowind's opening sequence starts in 16 Last Seed, 427, 10 AM. The dwarves disapeared in 1E 700. Yagrum Bagarn, the last dwemer in existence (from Morrowind), has been alive since the dissapearence of the dwarves, making him very very old. Guess what Tolkien race has a very long lifespan as well? Yep, dwarves.
The biggest difference between the two (Dwarves & Dwemer) is that Dwemer were very interested in science and magic, whereas Dwarves were not.