All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.
Firstly, the scholars differed in opinion about the ruling on abandoning the prayer; the majority of the scholars are of the view that it does not take a person out of the fold of Islam, contrarily to the famous view of the Hanbali School of jurisprudence.
Secondly, the majority of the scholars responded to the verse of Chapter Maryam in which Allah Says (what means): {But there came after them successors who neglected prayer and pursued desires; so they are going to meet evil.} [Quran 19:59]; in two ways:
1- There is a difference of opinion about what is meant by neglecting the prayer (that is mentioned in the verse). Some of them said that it means abandoning it totally, and some of them said that it means delaying it from its prescribed time, and some others said that it means forsaking its pillars, and so forth. They also differed as to what is meant by the word successors. Some of the scholars are of the view that it means people from the nation of Muhammad while others said that it refers to the Jews and the Christians ... etc.
2- The verse does not explicitly say that they will be eternally in Hellfire, as stated by Shaykh ash-Shanqeeti in his Tafseer (interpretation of the Quran). As for conditioning faith, then it does not mean falling into disbelief; one may deny faith from a person while he intends complete faith, and not that he does not have faith at all.
Thirdly, Ibn Mas'ood said: "Abandoning it (the prayer) is Kufr (disbelief)." [at-Tabaraani]
Al-Haythami said about it in az-Zawaa-id: "Al-Hasan ibn Sa’d and al-Qaassim did not hear from Ibn Mas'ood; so this statement is weak because of interruption (in the chain of narrators)."
Fourthly, by the Ahadeeth that do not permit rebellion against the Imam as long as he prays, you may mean what is narrated in the Hadeeth of the Prophet about rebellion against the Imam with the sword: "No, as long as they perform the prayer." [Muslim] The scholars said about this Hadeeth and other Ahadeeth that the Sharee’ah ordered the killing of those who do not pray, in the same manner that it forbade the killing of those who pray, and that what prevents the killing is the performance of the prayer. They said that all this indicates killing and does not indicate Kufr (disbelief).
Fifthly; the Hadeeth narrated by ‘Ubaadah Ibn as-Saamit is evidence used by the scholars that the one who abandons the prayer does not go out of the fold of Islam. Like other pieces of evidence, it is an issue of difference of opinion and others responded to it by what you mentioned in your question.
To conclude, the issue of the ruling on abandoning the prayer is a matter of difference of Ijtihaad and there is a difference of opinion among the scholars about it. Indeed, there was a famous debate between Imam ash-Shaafi'i and Ahmed, which some scholars reported from them.
If a person is a student of knowledge, he should act according to the view that he considers to be the preponderant one about it. In case he is a layman, then he should follow the Fatwa of the trustworthy scholars.
Allah knows best.