About infinitive after BUT.

Hi!
Is an infinitive with or without TO used after BUT , please?

Could you write the sentence you have in mind?

There is an argument between two people.
Person 1 posted an exercise and its key as follows


-The little girl had no choice but______ ____at home.　
　A. to stay B. to staying　 C. stayed D.stay

Person 1 says: If before BUT is a verb of non-action, after BUT is a verb with TO.
Ex:
- The Taliban have no other option but to negotiate with Afghanistan's government
- I have no other choice but to trust You That's all I can do
- Does Obama Have No Other Choice but To Threaten Iran?
- I have no other choice but to close the ask box for now.
- I have no (other) choice but to leave.(en.wiktionary.org/wiki/but )
- The first problem for all of us, men and women, is not to learn, but to unlearn.
- The most important thing in the Olympic Games is not to win but to take part

Person 2 says: According to PEU by Micheal Swan
The verb form after BUT usually depends on what came before. Infinitives are normal without TO.

Who is correct, please?

Swan says in that article, "Infinitives with to are used after no alternative/choice/option but." You have to read the whole article, not just select one sentence.