In some cases, that may be right, but in general branding begins the first time someone interacts with your product (or even your industry). If I notice your business name on Google SERPS, I am engaging with your brand.
I didn't really use NewRelic for 2 years after I first heard of it, but I did keep seeing them and speaking to them at events, reading blog posts, etc. Eventually, I signed up and paid for the product. What convinced me to do that was the branding work they did before I became a customer.
Even for freemium products, the business builds a brand to encourage people to invest the effort into signing up. Even government services (e.g. in the UK - the BBC, the NHS) do branding work.
Branding doesn't start at the point the customer enters their credit card.
Lovemarks is a good read on branding - http://www.amazon.co.uk/Lovemarks-Effect-Winning-Consumer-Re...
Also, you're not sending me your credit card number, you're sending it to Stripe, or Amazon, or PayPal. Regardless, I think you severely overestimating how cautious people are with their credit card info.