Surprising, isn't it? Actually, RAID does indeed increase failure rate. If you take MTBF, MTBF decreases with more disks. Even if RAID5, mean time between disk failures decreases.
In a fault-tolerant storage, time between failures (MTBF) does not matter. What matters is time between data loss events. This is called either mean time to data loss (MTTDL) or mean time between data losses (MTBDL).
You know you can setup a three-way RAID1 (three mirrored copies instead of two), i.e. the mirror can have more than two disks. So, let's imagine a RAID1 of infinite number of disks. This unit will have an MTBF of zero, because at any given moment one of the infinite number of disks is failing. It will also be continuously rebuilding while still delivering infinite linear read speed. Still, this imaginary device will have zero probability of losing data because of the disk failure, because the infinite number of disks cannot all fail at the same time.