That myth is an entirely different topic. Jobs was an accomplished salesman. He would tell the truth, but rarely the whole truth.
For example, he showed pictures of smartphones with keyboards, which was just one version of them. He talked about needing a stylus, which again was not always necessary. He also claimed that Apple invented multi-touch, which of course wasn't true at all. So we have to take things he said with a big grain of salt.
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By late 2006, everyone knew an iPhone was coming. That by itself was no surprise. Fan concepts were everywhere. We even knew that Foxconn had gotten the contract to make it.
As for the FCC, no sir, they didn't make it necessary to show the iPhone off in January 2007. In fact, it wasn't outed by the FCC until it got approval in mid May, FOUR months later.
Even then, all the important details were confidential. All that was revealed was the general shape of its back (where the FCC stamp goes), and that it was missing 3G. Nothing about the front or sides, or touch, or the UI. Heck, it could've used a trackwheel for all anyone could tell from the FCC.
Moreover, Apple could've kept it entirely secret right up until launch time if they had wished. That is what they did with the Verizon iPhone, which was publicly approved by the FCC on the same day that its existence was announced.
(You can ask for approval to be delayed until a day that you have requested. This keeps everything secret right up until you're ready to sell it. )
The upshot is, I think the real reason Jobs showed off a semi-working device six months ahead of time... an action that goes against all usual Apple secrecy... was because there had been demos of capacitive touch smartphones during much of 2006, and the yearly Barcelona mobile show was coming up in a few weeks. I think Jobs simply did not want his phone's debut to possibly get upstaged by another.
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