In business, every company believes they are #1; otherwise, they probably wouldn’t be in business. It is, obviously, a completely subjective assessment, just like the one at the top of your browser right now.
Nevertheless, when you claim to be #1, you usually do so because of the merits of your company and the value added you provide your customers and users. In most cases, you’ve proven to them that you are willing to reinvest in your business, regularly come up with new initiatives, and ensure them that while you’re growing (and increasing prices), that the services you provide are growing and doing the same as well.
Claim to be #1 - you deserve the right to do so. Just be sure you have a reasonable argument to back you up.