It's not unusual for hardware companies to work with chip companies. Nintendo works with their CPU suppliers to build a custom processor for their consoles. I doubt Steko is saying Apple taught Intel how to do chips right even though it came out that way.
While Apple probably didn't help Intel design the Core 2 Duo (they only had serious in-house processor design stuff recently, and it's ARM-oriented), it's quite possible they exerted pressure on them to make such a thing. The Core Duo and Core 2 Duo were a _major_ turnaround for Intel; they essentially abandoned the gigahertz at whatever price doctrine they'd been pursuing since the P4.
The Core Duo, in particular, was essentially _only_ found in Macs; it had very limited deployment elsewhere. It fits very well with the circumstances of the Intel switchover; Apple couldn't have used the P4M for its laptops (far too power-hungry vs the G4), or the PM (barely faster than the G4 at all, used somewhat more power).
Yes. The grandfather's post claimed Apple's CPU engineers were involved, and it is that characterization I object to.
Incidentally, as I own a Thinkpad with a Core Duo CPU (July 2004 T60p, SL8VN), I think it might have been more accurate to emphasize "essentially" rather than "only."
Yep; they did make it outside Apple, but only barely. There were a few products from other companies using them, mostly low-power laptops, and of course they lived on for a year or so more as a budget chip branded as a Pentium.