I do not think that is well grounded advice.
What's better, 2774 trials or 2592 trials? 2774 might be better, because it's more than 2592. What's better, 2775 trials or, say, 3888 trials? Again, 3888, possibly, but only because it's more, not because it's a multiple of 1296 (and only possibly, because the extra trials might be completely unnecessary).
If you do rollouts without variance reduction, the exact number of trials can make a difference (besides necessitating many more trials). Here's an example: in the rollout below, with 1295 trials and without variance reduction, the double/take result is slightly wrong:
The score (after 0 games) is: White 0, Blue 0
Move number 2: Blue on roll, cube decision?
| White | 2 | ||
|---|---|---|---|
                 | |||
| Blue | 7 | ||
| Position ID: AwAAEAEAAAAAAA Match ID: cAkAAAAAAAAE | |||
• Blue doubles
| Cube decision | |||||||||||||||||||||||||||||||||||||||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Rollout cubeless equity | +0.054826 | ||||||||||||||||||||||||||||||||||||||||||||||||||||
| Cubeful equities: | |||||||||||||||||||||||||||||||||||||||||||||||||||||
| 1. | Double, take | +0.109653 | |||||||||||||||||||||||||||||||||||||||||||||||||||
| 2. | Double, pass | +1.000000 | +0.890347 | ||||||||||||||||||||||||||||||||||||||||||||||||||
| 3. | No double | +0.054826 | -0.054826 | ||||||||||||||||||||||||||||||||||||||||||||||||||
| Proper cube action: | Double, take | ||||||||||||||||||||||||||||||||||||||||||||||||||||
| Rollout details | |||||||||||||||||||||||||||||||||||||||||||||||||||||
| |||||||||||||||||||||||||||||||||||||||||||||||||||||
| Full cubeful rollout without var.redn. | |||||||||||||||||||||||||||||||||||||||||||||||||||||
| 1295 games, Mersenne Twister dice gen. with seed 683107909 and quasi-random dice | |||||||||||||||||||||||||||||||||||||||||||||||||||||
| Play: world class 2-ply cubeful prune [world class] | |||||||||||||||||||||||||||||||||||||||||||||||||||||
| keep the first 0 0-ply moves and up to 8 more moves within equity 0.16 | |||||||||||||||||||||||||||||||||||||||||||||||||||||
| Skip pruning for 1-ply moves. | |||||||||||||||||||||||||||||||||||||||||||||||||||||
| Cube: 2-ply cubeful prune [world class] | |||||||||||||||||||||||||||||||||||||||||||||||||||||
Double/take equity should be 0.111111, and it's off by 0.001458. But with variance reduction, for this position, any number of trials (including 1295, or 1297, or 1) will get the right answer.
Rollouts with variance reduction do not need to be multiples of 1296, or even of 36. Timothy's comments are worthy, with regard to standardization (whenever that's important) and confidence intervals, but for all the difference the precise number of trials makes, one of the "small number of alternative" number of trials might as well be, say, 5180 or 5201, as 4 * 1296 = 5184.