No, intel didnt 'copy' AMD.
When P4 was made, the 'mobile' group who develop the laptop processors had a different goal, they wanted power efficient processors. So instead of following the desktop teams drive to Mhz, they kept working on the P3, developing it gradually.
And the did a good job, so good infact that people started to notice that a 1.6Ghz Pentium 'M' processor was doing almost as much work as a 3Ghz P4.
But still work carried on enhancing P4, adding extra cores, increasing the clock speed up to 3.73. But the desktop processor team hit a wall, no matter what they did, the P4 core wanted more power and generated far too much heat.
Mean while Pentium M was evolving yet again, into Yohan, otherwise known as Core Duo. Finally someone at intel realised that Netburst just wasnt delivering, and so they took the mobile 32bit Yohan core, allowed it to evolve into the 64bit desktop chip Conroe.
Its possible to trace out Conroes linage, and yes its a direct decendant of Pentium 3, but a lot of development lies between those chips.
Maybe we'll see netburst again one day, we'll certainly see certain aspects of it again, like Hyperthreading.