You are correct
if all the iPhone brought to the table icons in a grid that you tap and Three to four buttons at bottom to aid in navigation.
It had a deep and profound influence of the design of hardware and software on almost every device which had followed since.
I should add just to name a few. Even the design of the hardware and software wasn't anything new and sensational. The biggest and most revolutionary thing the iPhone did for the mobile market was make using a device with that many features easy and fluid.
Otherwise we'd still be trying to use Missing Sync, iSync, Docs2Go, Google, dotMac and a plethora of other apps, services, hardware, etc. just to get our smartphone to have the same information as our laptop. It was confusing and a headache 100% of the time, and it's what Palm and many other mobile device makers simply missed.
Apple hit the nail on the head and everyone knew they were going to be the ones to do it based on the iPod, iTunes, the Mac, and dotMac; we just didn't know when. When it finally came, we didn't expect it to be so darn good.
All in all, it shows how much attention to detail Jobs and Apple had. Claiming that they did influenced everyone else with a full screen slab of phone is almost short-changing their accomplishment. Apple didn't influence the mobile phone industry much on hardware and software design; if you dig deep enough it showed to be heading that way at least a year prior.
What they did do, which even (as an Android user) now no other company has been able to do, is make all the pieces fit together under an ecosystem that is truly in harmony.
Heck, I have to have at least 6 companies in my pocket or on my Mac just to get my Android
(HTC and Sprint) to sync my music library
(DoubleTwist), sync my calendar
(BusyCal), sync my email
(Apple), and to sync my files
(Dropbox). Now . . . who will I be calling when something goes wrong?
The iPhone . . . . . 2 at most.