Why are they doing this?

Thanks, Albert. Agreed.

To the OP, although I don't particularly recommend it, I'll mention another means of grounding the black wire, that MIGHT work acceptably, depending on the internal grounding configurations of the amp and the sub. That would be to connect the black wire to a chassis screw on the amp. I suppose there would be no harm in trying that, although the result might be a very loud hum. The RCA plug approach I suggested, though, is more technically correct and much less likely to have problems.

Regards,
-- Al

Very much appreciate the feedback here. To bring things up to date, I contacted REL and their answer was exactly what Al says here in the last post. Take the red and yellow wires, twist them together and attach to the positive post on each amp. Take the black wire and attach to a chassis screw for grounding. Ok, so that I don't seem like a complete idiot, the REL manual does show this connection for fully balanced amps and I DID look at it. My problem was that it shows only for a single sub and not monoblock amps. I didn't want to take a chance and connect them this way unless I was completely sure it was safe. So, that's the way their connected now and everything works fine. The led's are even metering again.
As for the suggestion to connect the RCA plug, maybe that would be a good way but I really don't think the folks at REL intended for anyone that bought their subs to have to go through those extra steps. I did learn soething here though and I thank you for that.

Just to let you know about REL subs as I have a pair of Stentors III connected to monoblocks. I use the red and yellow together for each sub on the + terminal of both right and left monoblocks so each Stentor is connected to one monoblock each. I do not connect the black wires. You only need to connect the black to ground if you have a hum.

01-31-14: Coxhaus
... You only need to connect the black to ground if you have a hum.

While with some amplifiers and subs not connecting the black wire will work, in general I would strongly recommend against it. As I'm sure everyone here realizes, for current to flow a complete circuit is required, in this case from the amplifier to the sub and back to the amplifier. Without the black wire being connected, instead of being through that wire the return path would be from the sub's circuit ground via some design-dependent impedance to its AC safety ground, then through the AC power wiring to the amplifier's AC safety ground, then through some design-dependent impedance to its circuit ground. In addition to creating a susceptibility to pickup of low level hum and noise, I would expect that to result in at least a few cases (depending on the internal grounding configuration of the sub and the amplifier) in hum that is loud enough to be destructive.

And particularly so in the situation where there is initially a low level hum, which the user then sees fit to try to eliminate by putting a 3-prong to 2-prong cheater plug on the power cord of one of the components. Thereby leaving the grounds of the sub and the amp "floating" relative to one another, with AC "leakage" paths (e.g. in power transformers) being the only means of signal return. I would not want to be anywhere in the vicinity in that situation.

Regards,
-- Al

Al, you responded to Albert's point about connecting a self powered sub to the linestage/pre as follows:

"[C]onnecting at line-level, which would require purchasing additional interconnect cables, possibly purchasing splitters and introducing them into the signal path, and possibly spending several hundred dollars or more on a buffer, while losing the possible sonic benefit of providing the same signal to both the subs and the main speakers, and introducing the possible sonic effects of the splitters or buffer, if needed, and of the additional interconnect cables ...."

Of course I get your points, which are fair. Just a few clarifications please. First, in my case, I suspect the sonic downsides may be acceptable because my linestage has two (2) XLR Main Outputs -- one for the power amp and the other for whatever turns you on. In my case, it's the self-powered sub. So the linestage's output signal did not have to be split. Instead, as mentioned below, it needed to be summed.

Second, while there may be some qualitative sonic costs to the hook-up just described, I suspect that it's minor because my sub is configured to blend into the fronts at about 40 Hz and below, which is the roll off point of the fronts. So .... the main signal from the linestage is direct, i.e., no artifacts, to the power amp and then of course to the speakers.

Third and last, I had no choice. My sub is NOT designed to accept an input signal from the power amp. Hence, a hook-up of some sort had to be made from the linestage/pre.

As you may recall from my posts about this issue some years ago, my impedance buffer had to solve three (3) problems at one time: (a) asymetrical loading of the linestage (i.e., XLR -- linestage to amp; RCA/SE linestage to sub); (b) summing the L and R channels without shorting the linestage's Main Outputs because I am running a single sub; and (c) increase the impedance presented to the linestage or else chance overloading the linestage's outputs, thereby causing possible sonic degradation.

Ergo, a custom impedance buffer designed and made by Tom Tutay (located in Ft. Walton Beach, FL). Considering Tom's fee, which was extraordinarily reasonable, he solved a lot of problems for a paltry sum indeed.

Cheers,