Danzou DID order Itachi to kill the Uchiha. How he collected the eyes after that is unimportant.
Jiraya/Tsunade/Orochimaru fought in the last ninja war, and they were very young. In the current manga I think Tsunade is like 60ish. Itachi is older than Sasuke but only by a few years. Here's a general timeline that I think makes sense:
35 yrs ago: Jiraya becomes jonin (15-20 yrs old, I would guess), trains Minato
30 yrs ago: Last ninja War. 3rd Hokage in power, Minato is Jonin in charge of Kakashi, Rin, Obito
28 yrs ago: Itachi born,
20 yrs ago: Minato becomes Hokage
16 yrs ago: Fox attacks Konoha (Naruto born, Sasuke born in similar time, they are the same age)
10 yrs ago: Uchiha massacre (Sasuke would have been about 5-6, Itachi about 18-19). Danzou gets most of his Sharingans
By this timeline, Jiraya was about 50-60 yrs old when he died, Kakashi is about 40-45. Itachi was about 25-30 when he died. Naruto and Sasuke are both about 16-18. We could even move the time of the ninja war up and make Itachi younger, but he must have been at least 16ish when he massacred the Uchiha (I would guess he had to be at least 18, but that's just a guess).
We know that Minato fought in the last ninja war, and that he was the team leader for Kakashi, Obito and Rin. We also know that Minato died when Naruto was born (at least 16 years ago). We know the Uchiha massacre happened later, when Sasuke and Naruto were about 5-6. So Danzou could not have had all his sharingans during the war.
This seems reasonable to me, but we don't have any confirmation that I am aware of.