Because is secured by the company and serviced by the cash flows from the company. Since the debt only exists if the transaction (acquisition of the target company) goes through it is really the company funding its purchase through the issuance of debt.

Btw you can get an SBA loan to purchase a small business. It works exactly the same way, and there are people who raise equity capital plus get an SBA loan to buy and run small companies, in effect they're running a very small PE deal and installing themselves as CEO.