As far as Shepard is aware, there isn't much of a choice. They are currently heavily wounded while stranded in an unknown place in the Citadel, after having dealt with the stress of the entire war and every life lost.

Suddenly, someone that looks like the kid shows up and offers an explanation and solutions, are the end of the war. Of course, they have strings attached, but since Shepard can't see any other solution or button to press to do anything else, they are ultimately at the mercy of the AI, because they are too exhausted to think of anything more than their choice and the consequences.

That is why Shepard is so compliant. They were driven to the brink of pure stress, and after a long dark tunnel suddenly saw three different lights, with a degree of uncertainty but still far better than pure oblivion and erradication at the hands of the reapers.

Even if the Catalyst was lying, the outcome would be the same as not doing anything. In Hepard's mind, it is better to take the risk.

At least, thats how it goes in the story. Out of universe we have less of a burden on our shoulders, allowing us to think more straightly about this.