Is it true that because WD green are low power drives which spin down when idle thus causing RAID controllers to mislabel them as dead when they cannot get data off of them?
No, WD green drives do not do this, at least not in the way you are describing. WD Greens do not spin down automatically, they only do so if commanded to. What they do do is unload their heads at idle, which can cause a small pause, but not enough for a RAID card to kick it out. Some people are concerned (I am not) that the head parking reduces the drive lifespan. On older models it was possible to use a utility to disable the parking, but as far as I'm aware new versions have removed this.
What WD Greens and almost all other consumer drives do not have is TLER or Time Limited Error Recovery. Other drive brands call it something different but it is effectively the same. What it means is that if a bad block is encountered the drive will try to re-read it several times, often for a few minutes if it is really bad. On a single consumer level drive this is a good thing, but to a RAID card it looks like a non-responding drive which it then kicks out of the array.
WD Reds and other "RAID version" drives do have TLER. When they encounter a bad block they will only try to recover for a few seconds, then they will report the error to the RAID card. The card will then recover from the mirror/parity data on the other drives.
As far as I'm aware there is no difference in the low level ECC between Reds and Greens, so their chances of encountering a bad block are equal assuming everything else is the same. What is different is how they respond when an error is encountered.
Also, do you have to have some kind of software that regularly checks the integrity of all drives in RAID
If you are using the built in Intel RAID there is a verify function, but I don't know if there is a way to schedule it automatically.
Many higher end RAID cards can check their data integrity automatically. My main file server has an LSI 9260 that has both a patrol read (check for bad sectors) and consistency check (see if the RAID parity makes sense) that can be scheduled automatically.