Is it just an old "wives tale" about how (even well filtered) oil "breaks down" after time and won't heat up as hot (or something like that) ?
All fats break down over time. Heat, burned bits, salt, oxygen, etc. accelerate the process. Shortening is much more stable than liquid oil. Even in liquid oils there is a wide range of quality with higher quality oils lasting much longer. Regardless of what you use, filtering is key to oil life.
On the other side of the coin, I know places that buy decent quality oil and dump it all every day and start over in the morning with fresh oil because they see doing so as a key to consistent quality.