"subsidy" and "externalized cost" aren't mutually exclusive concepts (as you hint at in "...because subsidies aren't just externalized costs" [emphasis mine]), so your semantic argument rests on shaky foundations. an externalized cost can be considered a subsidy in many contexts, including legal/political ones.
like most words, "subsidy" may have a more specific meaning in a particular context, but understood differently in a general context. so taking a stance that one definition is better than another is relatively futile (in the sense that it convinces no one who's not already sympathetic).
so rather than relying on semantics, make the argument you're really trying to make, which, by context, seems to be that you don't think externalized costs should be used in the comparison.
like most words, "subsidy" may have a more specific meaning in a particular context, but understood differently in a general context. so taking a stance that one definition is better than another is relatively futile (in the sense that it convinces no one who's not already sympathetic).
so rather than relying on semantics, make the argument you're really trying to make, which, by context, seems to be that you don't think externalized costs should be used in the comparison.