Why does the moon appear tilted?

[Jackamus]

TL;DR

Observing a waning gibbous moon at about 8.00am one morning it appeared that its direction of illumination, a downwards angle of about 45º, could not be coming from the sun as the sun was much lower in the sky.

Researching this I found that the usual explanation was that it was an 'illusion'. However this explanation, in my opinion, does not stand-up to the laws governing the transmission of light. I proposed that as light travels in a straight line this poses a problem for moon tilt.
Most of the explanations appealed to the curved lines on panoramic photos whilst others appealed to the great circle of an imaginary celestial sphere.
I used, as an example, a football illuminated by a bright light. It is easy to see the direction of the light from observing the illuminated part of the football and tracing back in a straight line to the light. Why cannot the same reasoning be applied to the moon and sun since it is only a matter of scale?

 

[russ_watters]

What? Do you have any documentation of this phenomena or did you just observe with your eyes? And it sounds like you are saying that the moon isn't illuminated by the sun...? Huh?

 

[Motore]

Here's a quick and easy to understand explanation:
http://chrisjones.id.au/MoonIllusion/

Also see this:
https://en.wikipedia.org/wiki/Terminator_(solar)#Lunar_terminator_illusion
https://www.seas.upenn.edu/~amyers/MoonPaper20June.pdf