Not true - you can 100% get into these positions without connections. As for the degree part, although this kind of job is likely a secondary position (as in previous PROFESSIONAL work experience) you can get to it without a fin/bus/econ/acct degree. For example, the kind of work he seems to be doing is closely related to Management Consulting work, in terms of the modelling and valuation. Consulting is a field you can enter from almost any degree, and in fact it's encouraged that you have diverse industry experience from an unrelated field.
Engineers, Doctors, Lawyers, Poli Sci's, they're all considered as candidates for MBB's (Mckinsey, Bain, BCG, ie the big 3 MC companies) as long as you have solid problem solving and number crunching skills.
He could have an MBA but I don't think it's essential.