Can I use a 23 W CFL in a fixture that's rated for a 60 W incandescent?
As far as I know, the only risk at issue here is of overheating of the bulb. The heat comes from two sources: the output and waste heat of the bulb, and from resistive heating of the fixture wires and switch and socket contacts. CFL bulbs draw less current and produce less heat for a given light output; however, they are far less tolerant of high temperatures!

Therefore, the rationale of the warning label may well be to warn that the fixture is not sufficiently ventilated for a CFL bulb above that power, even if the fixture is itself capable of surviving that amount of heat.

However, it is also quite possible that someone converted the "equivalent wattage" (which is a statement of light output and therefore almost completely irrelevant to power/heating) without thinking about it. I recently (2016) saw a lamp which had a claimed limit like "60W incandescent, 13W CFL, 7W LED". That's clearly just converting, and it's not going to be accurate for the wide variety of LED bulb types available.