I think this the least constructive kind of unhinged purity-based framing. You're right about one thing -- Mondragon isn't a cooperative; it's a federation of cooperatives. I note that the paper you linked to by Kasmir points out what the author sees as failings, but from my quick reading it does not say that Mondragon co-ops are not co-ops. I think you're on that branch alone.
But also, Kasmir seems to be faulting co-op members for some lack of ideological purity, and frankly, for failing to live up to the aspirations that others have built around them, which aren't their responsibility.
> Many academics and social justice activists alike — maintain that co-ops promise a more democratic and just form of capitalism and even sow the seeds of socialism within capitalist society.
> Co-op members voted to pursue an international strategy to open these firms, and, thus, to employ low-wage laborers. Hence, we are confronted with a complicated permutation of a familiar state of affairs whereby the privilege of one strata of workers depends upon the exploitation of another.
> Compared with workers in the standard firm, co-op members were less involved in and showed less solidarity with the Basque labor movement, which at the time was part of an active leftist coalition for socialism and independence for the Basque country.
But the point of a co-op is not to further the goals of academics and activists, nor is it the responsibility of any co-op to maintain allegiance to whatever movements or institutions that the author admires. If Richard Wolff wants people to vote in the workplace, and wants those votes to mean something, doesn't that power and autonomy also necessarily mean they have the power to disagree with his views and pursue their own success and flourishing? And its success should be measured by the degree to which co-op members benefit, not by the extent that they're an ideological tool for outsiders.
Yes, one might have wanted Mondragon co-ops to create other worker-run co-ops in other countries, rather than subsidiaries. But it's hard to see how that would have actually worked. Frankly, starting factories in China by talking to workers about how important democracy is could have gotten people hurt. And these firms do still need to be able to compete and succeed in a global marketplace in which most of their peers are operating from a purely capitalist playbook. If you draw your ultra-orthodox definition of what a co-op too narrowly, you risk adopting a definition which excludes successful firms of any significant scale.