Things happened as we saw on TV back in the day, without Clara or The Great Intelligence.
Then The Great Intelligence entered The Doctor's time stream and sabotaged his victories, in some unseen way. (Maybe one of those unseen sabotages was pushing The Doctor towards a different TARDIS, that wouldn't always take him where he needed
to be. That alone could make a huge difference to a great many civilizations he wouldn't have visited on his own piloting)
Then Clara popped into the Time Stream and she undid The GI's sabotage, by directing The Doctor to the right TARDIS or any other thing a Clara might do to set time back straight.
One Day I hope to be the Man my Cat thinks I am
Where are we going? And why are we in this Handbasket?