What browsers would those be? Do they actually render the HTML on the phone, not on remote servers like Opera?
I would like to see a FireFox or Chrome iOS browser. . . But they are WebKit based.
Per the articles I linked, that's by Apple's design. They currently restrict HTML rendering to using their engine only, based on what I linked (and one of those links is from just last month).
Changing the definition to fit your needs? Opera Mini allows you to browse the web, thus the term web browser is fitting. The issue of Opera using a proxy is irrelevant. By this logic, most corporate Blackberry users don't have web browsers because they go through the BB Enterprise Server, which has a function called MDS Connection Service. That service can do much of what the Opera proxies do, including format conversion for the Blackberry Browser. That Opera can't faithfully live-render full standards such as HTML5 and CSS, interact using AJAX or pass the ACID test is irrelevant, since a lot of web browsers can't do that either. Opera Mini/Mobile isn't just a web browser, it's a web-browsing system that can speed up your low-bandwidth browsing immensely and help keep you under your data plan's cap.
I'll agree if you want to say the iPhone has no non-WebKit integrally standards-compliant web browser. That is a limitation. Then again, WebKit is by far the best standards-compliant platform for web browing on mobiles, so you aren't missing anything.