In all of the testing I've done and in all of the screen shots I have seen I have never once seen a peak or maximum temperature reported by RealTemp that was an inaccurate spike. Not once.
I can't speak for Core Temp but I know the data coming from the Intel Core temperature sensors do not ever spike up unless the core temperature has spiked up.
Maybe he thinks that the rapid increase in core temperature when you go from idle to full load is some sort of mistake. It's not. The core temperature really does go up or down very rapidly when a big load like Prime95 or LinX is started or stopped. When you instantly flow a lot of amps through something the size of your finger nail, of course it is going to heat up very rapidly.
It's easy to say, "RealTemp and Core Temp are a dog's breakfast" but if that is true then ask him to show an example of this. We can't speak for Core Temp but you and I both have enough experience with RealTemp and reading core temperatures that we know his statement is not true. I don't know how to convince him how to do some proper testing of this.