Good approach, I think.

The commenter is saying that with our current glosses, 炎を受け付けません could be wrongly translated as "not withstand the fire" (the opposite of the actual meaning).
This is a tricky one because glosses like "bear" or "tolerate" are perfectly fine in other cases (e.g. "胃が弱くて, 油っぽい食物を受け付けない.　My weak stomach won't take/tolerate fatty food.")
But in the commenter's example they're ambiguous. You could interpret "not bear the fire" as meaning either "not be exposed to the fire" or "unable to endure the fire".
The same goes for this sentence in GG5: "この新型の装甲車は通常の対戦車砲の弾などまったく受け付けない.　This new armored car will completely withstand normal antitank weaponry."
I think having an extra sense is the way to go but it's probably best to avoid glosses like "to refuse; to reject; to resist" (that only work when the verb is the negative) because it creates confusion.
I've proposed a new sense based on the "to be affected by" suggestion.

@@ -32 +32,3 @@
-<gloss>to withstand</gloss>
+<s_inf>usu. in the negative</s_inf>
+<gloss>to (be able to) take (food, medicine, etc.)</gloss>
+<gloss>to bear</gloss>
@@ -34 +36,8 @@
-<gloss>to bear</gloss>
+<gloss>to endure</gloss>
+</sense>
+<sense>
+<pos>&v1;</pos>
+<pos>&vt;</pos>
+<s_inf>usu. in the negative</s_inf>
+<gloss>to be affected by</gloss>
+<gloss>to take damage from</gloss>

Isn't saying that they'd *resist* the flames while they were petrified? This verb is often used in the negative to mean reject/refuse, e.g. GG5 has:
受け付けない 〔拒絶する〕 refuse; reject; turn down
I guess it's not clear that here refuse/reject/turn down/resist is the opposite of accept/receive/etc. We could have entries for 受け付けない and/or 受け付けません, or we could have another sense "(in the negative) to refuse; to reject; to turn down; to resist".
What do others think?

大辞林 + 大辞泉

I have this game where a magician has decided to save everyone from burning to death by turning them temporarily into stone, and she explains why with this line:

「少しの間　石になっていてもらいます。
石になっている間は炎を受け付けません」

I believe the translations of sense 2 here are completely the wrong way around. You would get the impression that they would NOT withstand the heat when they are petrified. But this is of course the opposite of its correct meaning.

I don't know how to fix this.

I came up with "to be affected by" "to take in" but that's it.

GG5 (splits sense 1)

@@ -25 +25 @@
-<gloss>to be accepted</gloss>
+<gloss>to accept</gloss>
@@ -26,0 +27 @@
+<gloss>to take up</gloss>
@@ -32,0 +34 @@
+<gloss>to bear</gloss>