Check out Modal’s impressive compendium of drop chance info instead of this thread:
It does not discuss legendary/epic drop chance, but it does show (with exact percentages) how the odds of finding magic/rare/double-rare items is affected by challenge layers.
Some exact percentages:
There’s also a link to a spreadsheet where you can check the chances for specific affixes and items.
Bottom line: Tougher challenge layers do make it more likely to find those double-rare items.
Whether the improvement is “significant” is up to you, but in the linked example the odds of a boss dropping a yellow-yellow item (likely useless) drops by 75%, while the chances of dropping a green-green (double-rare) item increases by 25% in the hardest dungeon types. (But a 25% increase on a terrible base chance is still a pretty terrible chance.)