Hard to say whether Apple (and the other companies mentioned below) were lying or not. You could imagine that Apple was not working on X at the time but later decided to work on X. And no, some individual engineer tinkering away in the corner inside the company without any support is not the same thing as the company working on X.

Did they?

No video iPod: http://www.engadget.com/2004/04/29/steve-jobs-says-it-again-...

"People don't read anymore": http://www.wired.com/gadgetlab/2008/01/steve-jobs-peop/

I'm pretty sure Jobs was quoted at some point shooting down the idea of an Apple phone, but it's nearly impossible to Google for that amid the Antennagate results.

Yes. And so did google.

http://news.ycombinator.com/item?id=1706814

I know Google did, e.g. here's a 2007 story on that: http://www.expertreviews.co.uk/general/108490/google-denies-...

I can't find any explicit denials by Apple, though. Digging through some 2005-2006 news archives, I find Apple denying some specific rumors, but neither confirming nor denying whether they would come out with a phone in general.

They (Apple) were actually working on a phone in 2005 which they announced in September of that year - the first "iPhone" before the iPhone - http://direct.motorola.com/hellomoto/rokr/. Of course, that turned out to be a crapfest noone was happy about and Jobs couldn't help wincing even while presenting it.

And Google about the Nexus One.