Not true.
While apps that already ship preinstalled on the iPhone are indeed native, a lot of third-party apps are native as well.
What 'native' means is that they were actually coded in Objective-C (the iPhone/iPad/Mac development language) to increase speed of the app etc.
This is opposed to non-native apps that basically have to redownload the objects on the screen over again every time you launch the app. This wouldn't be coded in Objective-C but in e.g. HTML5 (a web development language)
Think of the Facebook app (pre 5.x version) - it was basically a mobile web browser that only functioned as Facebook. I don't know if you paid close attention, but every now and then there would be something different looking in the Facebook app, like the way you comment or 'like' something. This is what non-native allows you to do. Change things without the user actually having to update through the App Store. But this comes at the cost of app speed, which is why users were getting a slow and frustrating experience.
Now the Facebook app is native, and albeit much faster than before, they cannot update the app for everyone on their end anymore. They have to release an update in the App Store and then we, the users, have to update manually.
Non-native lets your run a lot of A/B testing. For all you non-technical folks out there, this means that the developer can test out to see 'what really works or not' for the end user: monetization, user engagement, activity, response rate, all the good stuff etc.
This is what I suspect happened to the Facebook app. People complain 'oh it took them 5 years to release a native app'. They have been A/B testing this whole time, not being lazy. Facebook in particular had struggled to monetize on mobile, and now that they believe they've found a potentially successful way - they release a fast, slick native app.
Same goes for the YouTube app. These two in particular are huuuuge platforms and 'getting it right' is important from the start.