I doubt the PS Eye is the only reason. The Eye is only $60 retail so it seems highly unlikely that it'd add a further $100 for the asking price of the PS4.
Microsoft decided to make one giant chip of an APU with CPU, GPU and ESRAM in a single chip. The ESRAM on its own takes up 1.6-2.15 billion transistors (out of the 5 billion for the chip). With a chip of that size and complexity it's no surprise the manufacturing costs are going to be high. Keep in mind that a single 7970 GPU (which is AMDs top line GPU) contains 4.3 billion transistors and at release retailed for a little under the cost of a X1. That's without all the added extras of optical drive, PSU, HDD, case etc.








