A smartphone is a device that combines computer and network/internet capabilities with telephony. The definition is not about feature differences (e.g., physical versus onscreen keyboard), popularity, etc. There were several devices that met the definition of a "smartphone" before the Apple iPhone came along. The argument that Apple "invented" the smartphone is therefore, yes, silly.
An airplane is a vehicle that carries passengers or cargo across the air. Who invented that? Most people (including NASA) would argue: the Wright brothers, of course. But by your logic, you could equally make the case that it was Leonardo da Vinci.
A hundred years from now, nobody will care about the Nokia Communicator or Palm Treo and other proto-smartphones. They'll call Apple the inventor of the smartphone, because Apple made the leapfrog product that changed the category from niche novelty to mainstream.
(I've also heard the smartphone defined as "unlike a feature phone, it allows you to install third-party apps", which means the original iPhone may not even apply. But, again, none of these nuances will matter in the grand scheme of things.)
Look at how much Apple cut the price of the iPhone in the months and years after original launch. The original 8GB iPhone launched at $599 but a year later, the price of the 8GB iPhone 3G was just $199. Had Apple (and AT&T) not drastically cut prices, it may have been a different ballgame in the smartphone world.
This is somewhat misleading, as those are subsidized prices. Once you factor in subsidies, the difference is less stark. By today's price model, the 3G would absolutely not be $199.
Having said that, it's also really not relevant. "The iPhone is a high-end product" is not a relevant argument as to whether it is the product that changed smartphones for good. Mercedes-Benz by and large doesn't make mass-market cars (and arguably never did), but nobody is arguing against Karl Benz having a significant contribution to defining today's automobile.