(sorry but the quote link is not working for me, I’ll do it the good old way)
I would say the conclusion assumes there is no interaction whatsoever between separate 3 groups of 7 workers
That is the constant return to scale (or homogeneity of degree 1) assumption. As you said, more scale implies that maybe “the groups share various facilities and services”. But if you have increasing average return for any quantity b of one factor B while keeping the quantity c of the other factor C fixed, by the act of adding more Bs you’re in a sense scaling also (specifically, in the sense that sharing facilities for more Bs is now possible while at the same time the process produces more output more efficiently), although not preserving the original factor proportions. It’s very difficult to me to imagine an scenario where you can always increment b alone to get a more efficient production process and at the same time proportional scaling of b and c would have been a better choice. Generally speaking, the point is that in order to share facilities you increment b but -as usually you have to deal with diminishing returns to one single factor- you are forced to increase c also, and this way increasing returns to scale is rationalized. However, in the case that C is not a bottleneck -and moreover that the same C is better exploited by more than by less Bs- it seems not very credible to assume increasing return to scale, IMHO. Now, Mises posits increasing p/b just in order to disprove it by reductio ad absurdum and, because of the above, I think non-increasing return to scale is a reasonable additional assumption in this specific context. Of course, what you object is mathematically valid.
Also, there is an assumption that the business is small enough not to affect the market by its scaling.
This is just a technological issue, market plays no role up to this point, there is no costs or benefits involved but just physical inputs and outputs.
how does the theory of diminishing returns address the fact that some resource may be complimentary to itself?
This is not a theory of diminishing returns, this is the “law of returns” which accepts increasing (both marginal and average) returns to factor B up to an optimal point, for fixed c of C.