Did the White House get its name from being burning down in the war 1812? Truly? Is there a reputable source?

I've researched this extensively on the internet and a number of sources say that the Brits/Canadians marched down and burned it to the ground. Subsequently, the Americans painted it a brilliant white to try and cover the memories of the embarring military incident. This is one origin of the name that is out there. Others discount this story although part of me wonders if Americans are trying to rewrite history. Are there reputable historical sources, preferably non-American that exist? Is there a definitive answer that exists? I'd like to settle this.