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So, Swarms take two wounds for every failed save from a template/blast weapon.

Overwatch allows d3 hits from template weapons, but the actual template is not placed.

I'm the one using the swarms in question, and from my (quick) read of the rules, it's the weapon type (not the actual plastic aoe marker) that causes the "double wounds on a failed save" clause to be triggered, and that since a template weapon causes the overwatch d3 hits, any failed save with a charging swarm would lead to two wounds on the swarm base.

In other words, I'm never charging swarms into a unit with incinerators ever.

Does my argument hold water, or am I wrong?

You would be correct as the Swarms rule does not say under the blast/template but by any weapon that is a blast/template weapon.