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.
The vast majority of ads for luxury cars, for example, aren't going to elicit an immediate purchase, but still provide value for the automaker down the line.
Obviously the ads have to eventually lead to sales, but an immediate and trackable sale isn't always an option.