> A statement that there are no peer reviewed articles about X's efficacy should be sufficient.

Unfortunately, this doesn't leave the reader with much confidence, our motto here being [*De omnibus dubitandum est*][sk]. I think your argument rests on several good observations: 
  
1. Theoretically, it is generally not possible to prove that *no research has been done*.  

2. Realistically, where there is no plausible association, it is unlikely to find research statistically "proving" the absence of an association (although this, it should be said, is theoretically possible).  

To me it does not follow that `a statement that there are no peer reviewed articles...should be sufficient`. I can think of several approaches that would be considerably more helpful:

1. Consider the theoretical basis for the claim, and provide evidence about the relevant physiology. This may include review articles or textbook chapters explaining "how things work". Undercutting the physiologic plausibility of a claim can be a substantial counter-claim. 

2. Provide evidence for standard of care or consensus recommendations for X condition, and show that Y treatment is *not in the picture*. Showing that experts in the field do not consider Y worthy of inclusion in such an overview is also a substantial contribution against an absurd claim. 
  
Both of these* are methods of approaching a Health.SE question of this brand without eschewing the need for evidence altogether.  

<sub> *This is not to say that these are the *only* methods -- this is just what I can think of off the top of my head. Creativity is encouraged.</sub>

[sk]: https://en.wikipedia.org/wiki/De_omnibus_dubitandum_est