"The Italian monk Guido d'Arezzo introduced four horizontal lines in the early 11th Century, with a yellow line marking the position of C and a red line indicating the position of F"

Not quite right - as I remember it these four lines represent the first four notes of what we call the Dorian mode today.

If we work backwards from the subsequent premiss that C is the only key with no sharps or flats then we would be dealing with D dorian, and might retrospectively assign the notes D, E, F & G, however this would be to view their system in hindsight and would not be an accurate description of how music was understood at the time.

I will return with more info later when i have had some sleep.