Almost.
12A*7 family tubes are dual triodes, which means they have two stages inside of them. That's the first part of the explanation.
The clean (blue) channel of Detective uses two of the available 4 stages (2 stages x 2 tubes = 4 stages). The red channel actually shares the first stage with the blue channel, and uses the additional 2 stages on the end, so it's a total of 3 stages. All of these are set up as gain, none of them are buffer stages.
Dr. Wattson also has 4 stages available, but it only uses 3 of them, again all set up for gain. I actually tried tacking a buffer on the end to make use of the extra stage, and I hated what it did to the sound. It could have just been a poorly designed buffer, but either way I pulled it out, and Dr. Wattson has always only used 3 stages, the 4th stage is completely unused.
And now everyone knows the dirty little secret of wasted tube stages on Dr. Wattson.