They probably overpaid, and overpaid by a lot, and trumped-up the figure to make headlines. But they could not have done it in a proper way for $100, either.
What exactly did the FBI pay for when they hired this company to crack the phone?
I mean how many PhDs helped design the tool set used. (This was an in house developed system)
How much for the guy who's using it and doing the work?
Compute time on hardware that is custom designed? (Even with COTS hardware there is always some tweaking)
All of this is part of the cost.
And again, there is a time value to the solution. Could the FBI and NSA build a comparable solution?
Sure, but it would take N months of X man years of resources, plus the hardware...
And that's why you see the $$$$ being charged. Because they can do the following:
1) Show value
2) Cheaper than the alternative
3) Have a solution in place
4) If they failed, there was always a riskier plan B of pulling the chip.