This exactly. Try for yourself. Personally I find myself more creative when I don't use caffeine - being slightly tired may even help a little. However, being slightly tired does not help with my more normal, non-creative, work.
A former coworker was just the opposite - put a few espressos in him and the creativity almost oozed out.
The idea is that some types of problems are best solved with the focus you can provide at your peak times of day. However, "insight" problems might benefit from the reduced focus you have at non-peak times.
My worst screw up was causing a fire that destroyed one of the two prototype 3D printers my company had built.
I was working at a startup that was trying to create an affordable 3D printer. We had two working prototypes that were used for everything - demos, print testing, software testing, PR shoots, everything. Each prototype had cost hundreds of man hours to build and debug and quite a bit of cash as well.
Among other things I had done all the work on the thermal control system for the printer, it kept the print heads and build chamber at the correct temperature. One night while working on one of the printers I hit an edge case that my control code didn't handle well and the printer turned all of the heaters on full-bore. Half an hour all the plastics in the prototype had either melted or burned and I was left with a room full of smoke and a pile of scrap aluminum.
A former coworker was just the opposite - put a few espressos in him and the creativity almost oozed out.