When defined broadly Douglas' theorem that loans create deposits is tautological and irrefutable. A useful analogy or metaphor to dynamically accumulating balances is a theoretically perfect pipeline in continuous flow from well-head to refinery. So long as the pipeline remains in operation the pipeline contains a definite volume V defined by its dimensions, length and diameter. But imagine an expanding pipeline with expanding dimensions. It is not an illusion but empirically confirmable fact.
Much confusion arises from muddled or conflated definitions.
Disbursement is not synonymous to cost, and cost is not synonymous to expense. A disbursement to repay the principal of a bank loan is neither a cost nor an expense. The proceeds from a loan is not income. Every cost is expensed but not necessarily simultaneous to the cost. It is a useful fiction in that it supplies an objective criterion to judge the relative productiveness of the entrepreneur without excessive bureaucratic oversight and regulation.