That makes no sense at all. I have worked for companies large and small, utterly dominant or not it doesn't seem to make any real difference to the company culture. That is what we are talking about here, there will always be the odd person that oversteps the line in any company but ignoring those some companies like Intel and Nvidia have a "win at absolutely any price" culture, many companies don't.
But then I think Nvidia were a nicer company before Intel trashed Nvidia's chipset business, blocked the Atom graphics booster line and shut down any attempt to make an x86 competitor etc. If Intel were gunning for me, I probably wouldn't be very nice either.