Tabs within tabs are confusing because it's hard to figure out where you are; each layer of tabs ads a spacial dimension. For more info on what makes tabs within tabs problematic (and how to avoid the trouble), see Is there evidence to suggest that designing tabs within tabs creates a bad user experience?
However as you note, tabs are common in webpages. Why wouldn't these tabs be fine?
The problem of "tabs within tabs" is obviated by the clear distinction between page and browser. Your user is almost certainly very familiar with where the browser tabs stop and the page starts, unless you're trying to make the tabs identical to the user's browser's specific tab style, your app's tabs will be in a clearly different context from the browser tabs.
Since the context between browser and page is clear, you're losing the big problem of tabs within tabs; nested, branched navigation.
Take a look at Tabs, Used Right. Specifically you're using tabs for view-switching, and presumably in-app there's really only one row of tabs. As long as you're keeping to one row of in-app tabs it shouldn't be a problem because contextually it's quite clear that those are your apps tabs, and there's no navigating back and forth between multiple layers of tabs in the same app.