This is actually quite a good question, and I don't understand why you're being given such grief for it. But I also might have an answer. TL;DR: the government isn't paying McKinsey for services rendered. It's paying for bureaucratic capital, which is a Veblen good.
There is a confluence of two dynamics going on here. The first is that once a contractor is listed on the GSA schedule, you don't have to justify their price. The process of getting listed on the GSA Schedule is supposed to mean that the government has already vetted the goods being offered and the price they're being offered for. No further competition is needed. You can simply place an order for the goods or service listed and like magic it sails through the government procurement process.
So the next question is, if contractor A and contractor B are both listed on the GSA Schedule as providing a given service, and contractor A is twice as expensive as contractor B, why would any rational individual choose contractor A? And the answer is, in this case, you aren't paying for the advice. You're paying for the social capital needed to make the advice stick. If all you wanted was the advice, you could certainly go to contractor B and pay them twice minimum wage to get a 23-year year old college graduate to give you advice. But that advice would not carry the weight you need to get upper management to take it as gospel, because you clearly didn't pay enough money for that. Nobody cares if you pay $50,000 to get consultant advice and then ignore what they told you.
So what you do instead is pick the name with the most cachet out of the entire list, given that you don't have to justify the price on a cost-benefit curve any more since it's already been GSA approved, knowing full well that they'll give you identical advice but now with a million-dollar price tag attached... and that fact will carry enough weight to get the changes they recommend all the way up to your agency director, who'll either sign off or have to take an incredible amount of public heat explaining why he/she didn't take the advice his/her own agency spent millions of dollars to get.
Basically, a straightforward application of the Washington Post rule.