It's correct that the number of reinsurers is smaller than that of primary insurers. But the risk born by reinsurers is less correlated, not more. Any given primary insurer has risk clusters (domestic market, line of business, etc.). If a large catastrophe happens in their domestic market they might go bust but what are the chances that it happens simultaneously to all markets globally?

Say you're a primary home insurer in the US. If a hurricane hits you might not have enough capital to rebuild all the homes. A reinsurer which is also covering Europe, Asia, LatAm, etc. is less likely to go bankrupt. The reinsurer can cross-subsidize and use the insurance premiums from other regions to pay out the claims from the US market. All that matters is that on average the loss probabilities and severities are estimated correctly.

And this is just using one line of business as example, reinsurers are covering property, casualty, life and health which add extra layers of diversification.