You do need to understand the concepts of invoices, credit, tax periods, pro-rata billing changes and so on... but all of that knowledge can be used to make an informed decision on build vs buy, rather than an automatic reason to outsource.
The only external API you need for software-as-a-service is a credit card processor, two if you're fancy. Sure after the first year you will probably have a bunch of manual work to do and your accountants will tell you the dumb stuff you've done, and you'll learn a lot about accounting :)
(I would still shop around to start a new business today, but with the confidence that building isn't very scary)