Having sold digital goods for years, I can attest that this is not true. For example, customers have questions, which consumes one's time. They do returns. Fraud costs. Accounting costs. Taxes on transactions. Bandwidth costs. Hosting costs. Transaction fees from your merchant service account. Etc.
I guess it would be more accurate to refer to the cost of producing one more month of service rather than one more customer. Even then there are costs, but they're tiny compared to the costs of providing a physical service.
Contrast the costs of running Netflix now vs Netflix when it was distributing DVD's in the post (or the costs that Blockbuster had). Adding one more customer to Netflix costs so little now that it's effectively zero, compared to the direct costs of sending out DVD's in the old days.
Ever notice that online companies hide from their customers? As in, no phone number, no email address, no way to contact support, they just direct you to a FAQ. This is because customer service is very expensive to provide.
It costs nothing to produce one more unit of a digital good (or add one more customer to a digital service). Prices in economics are affected by supply, and supply is limited by the marginal cost of production. If there's no marginal cost, then there's no limits on supply, and price tends to zero.
Startup economics agrees with this. If the cost of acquiring a customer via paid advertising is $9.99 and the lifetime value of a customer is $10, then the smart thing to do is to spend every single dollar you can raise on paid advertising (I exaggerate slightly). The value we place on the actual production of that service for each new customer is zero.
This completely messes up traditional economic models.