but privately, the stunt stung

[GoodTaste]

The Megastate G.O.P. Rivalry Between Abbott and DeSantis
Publicly, Gov. Greg Abbott of Texas has not criticized the migrant flights orchestrated by Gov. Ron DeSantis of Florida — but privately, the stunt stung.

Source: NYTimes

I understand "the stunt stung" as "the fight/rivalry between the two governors hurts/is fierce/painful". Am I on the right track?

 

[SoothingDave]

There is no fight between the two governors. That's the point. Privately, Abbott did not care for DeSantis' Martha's Vineyard "stunt," but he is not publicly criticizing. Abbott felt it "hurt" whatever position that he was maintaining in dealing with the federal government's failure to enforce the border.