Does quark confinement imply indivisibility of quarks? I recently heard the statement$^1$ that quark confinement is evidence for the indivisibility of quarks (i.e. that they are indeed fundamental and have no substructure), but I don't see any reason why this should be true.  Is there any merit to this statement?

$^1$ Science and Dissent in Post-Mao China: The Politics of Knowledge" by H. Lyman Miller, p162. 
 A: Here is a review from the particle data group of searches for  compositeness for quarks and leptons. . It is from 2001 but I suppose that they are not updating it since it gives the basic parameters for their table of limits for quark and lepton compositeness (2015).
In the review the word "confinement" does not appear, as it necessarily would have, if confinement were a necessary and sufficient reason for the elementary nature of the quarks. There is no evidence that quarks are not confined at present. There are theories where quark decays will violate baryon number conservation, thus leading to proton decay, but that is another story not involving confinement.
As the link provided is from twenty years ago, from within another physics subculture, probably it has to do with a particular theoretical proposal that has not emerged in the western story line of quark compositeness. I would trust the western version, as our experimental results are surely valid.
Here is a review of theory on confinement 

Quark Confinement: The Hard Problem of Hadron Physics

"Compositeness" is not found within it either. It does speak of :

It  is  odd  to  have  a  complete  theory  of  one  of  the  four  well  established  forces  of  nature the  strong nuclear  force and  still not have general  agreement,  after  more  than thirty years  of effort,  on how that force  really  works at  long distances.

A: The answer is no, confinement does not logically imply indivisibility.  There are models of particle physics -- generally known as preon models -- in which quarks are composite.  
