I think that the "equal terms" is coming from the adverbs such as 互角に and 堂々と. If it was implicit in 渡り合う, why would they be added? Both the JEs and kokugos have them.

@@ -17 +17 @@
-<gloss>to fight (with) on equal footing</gloss>
+<gloss>to fight (with)</gloss>

sankoku:
たがいに（対等に）〈切り合う／戦う〉。
daijr:
相手になって争う。応戦する。
「チャンピオンと互角に━・う」
meikyo:
相手になって戦う。
daijs:
相手になって戦う。
「格上のチームと互角に―・う」
obunsha:
刀できりあう。また、激しく競い合う。
「強豪と互角に―」
iwanami:
相手になって切り合う、または争う。激しく論じ合う。
「互角に―」
koujien:
相手になって斬りあう。（強い相手と対等に）戦う。
gg5:
►互角に渡り合う　prove oneself ┏a match [a worthy opponent, no mean foe]
・堂々と渡り合う　compete [vie] fairly and squarely 《with…》

i don't think it's over-interpreting
sankoku and koujien explicitly say that it's fighting on equal terms, most kokugos use "相手になる" which basically means the same thing in this context and generally all dictionaries go out of their way to use "互角に" in examples

@@ -17 +17 @@
-<gloss>to fight (with)</gloss>
+<gloss>to fight (with) on equal footing</gloss>

That qualification isn't in any of the JEs. I think it's over-interpreting what's in the kokugos.

@@ -17 +17 @@
-<gloss>to fight (with) on equal footing</gloss>
+<gloss>to fight (with)</gloss>

sankoku, daijr/s, smk

@@ -17 +17 @@
-<gloss>to fight (with)</gloss>
+<gloss>to fight (with) on equal footing</gloss>

"debate" seems a bit tame here. I think it should go further down.

@@ -25 +24,0 @@
-<gloss>to debate</gloss>
@@ -27,0 +27 @@
+<gloss>to debate</gloss>