I originally wrote something to the effect of "BigCos are never going to pay you up front", but tried to go back and edit my comments to hedge this, knowing that someone here would have some kind of counterexample.
I don't have a black and white rule here; I'll just say two things:
* BigCos usually have payable processes, and if they do, your contact at the BigCo is unlikely to have the authority to short-circuit them unless your service is so cheap that they have direct signing authority for it. Otherwise, what you're fighting with the payment-upfront negotiation is the friction it takes to change any part of a BigCo's "how do we release invoices for payment" process. If anyone with title =~ /purchasing/i is involved in your negotiation, give this up.
* Equally importantly, the payment upfront clause mitigates a risk you mostly don't have with BigCo's. Upfront payment is earnest money. You need earnest money when the amount of money you're working with is large enough to be worth your client stiffing you over. For a BigCo, almost any first project you do is going to be worth less than that amount; your $15k web project is a rounding error to them, and any real dispute over payment is going to cost them more than $15k in the end, and they absolutely know it.