I was just listening to the young lady who called in on the 16 August 2008 show about her 2004 Mazda. The problem she described was that when she put the car into reverse, it would only half-way engage until she let out the clutch just a bit. This made the transmission emit a grinding sound.
I have the exact same “problem” with my 2004 Hyundai Elantra. The young lady was advised to “slam” the shifter into Reverse gear, but I assure you that it won’t do a bit of good unless she lets out the clutch a very slight amount.
The good news is that, when this happens, all she needs to do is let out the clutch until it only just starts to engage–not even enough to cause any movement from a dead stop in first gear, only enough to tickle the transmission–and the gear will slot into place. I don’t know if this is altogether normal, but by adjusting the speed with which she lets the clutch out, she should be able to avoid the grind.
You and she aren’t the only ones to experience this problem. Whenever it happens to me, I use the procedure you outlined. What it does is to rotate things in the transmission enough for the gear to engage.
My owner manual says the same thing. Be careful when starting the engine cold. Shifting to reverse immediately after clutching in = nasty grind. I’ve done that a few times. Simply letting off the brake and let the car roll a bit helps too.
Reverse gears rarely have synchros, like all forward gears. Sometimes, the teeth are just lined up and hit tooth to tooth. Letting the clutch out moves everything so it can engage tooth-to-slot
In that situation I usually hold down the clutch, then while holding it down I put it into 1st, then into reverse. YMMV but it works every time for me.