From the "Great References" sutta (AN 4.180
), the Buddha taught us the proper way to handle claims made by other people:
a bhikkhu might say: ‘In such and such a residence several elder bhikkhus are dwelling who are learned, heirs to the heritage, experts on the Dhamma, experts on the discipline, experts on the outlines. In the presence of those elders I heard this; in their presence I learned this: “This is the Dhamma; this is the discipline; this is the Teacher’s teaching!”’ That bhikkhu’s statement should neither be approved nor rejected. Without approving or rejecting it, you should thoroughly learn those words and phrases and then check for them in the discourses and seek them in the discipline. If, when you check for them in the discourses and seek them in the discipline, [you find that] they are not included among the discourses and are not to be seen in the discipline, you should draw the conclusion: ‘Surely, this is not the word of the Blessed One, the Arahant, the Perfectly Enlightened One. It has been badly learned by those elders.’ Thus you should discard it.
Then from the "Elements" discourse (MN 115
), the Buddha taught this truth about Fully Enlightened Ones (SammaSambuddha):
It is impossible, it cannot happen that two Accomplished Ones, Fully Enlightened Ones, could arise contemporaneously in one world-system—there is no such possibility.
which Ven. Bodhi further explained:
the Pali commentary associated with the above text from MN 115 states: The arising of another Buddha is impossible from the time a bodhisatta takes his final conception in his mother's womb until his Dispensation has completely disappeared. The problem is discussed at Miln 236–39. The referenced Milindapanha section is entitled, Ekabuddhadhāraṇī - pañho
Bottom line is, though many masters from various schools claimed their attainment of "Buddhahood", per the suttas' teaching, it doesn't mean they have attained "Fully Enlightened" Buddha state for the Dispensation is still around. If they meant the state of Savakabuddha or Arahantship, then any Buddhist school would be just as good provided that its practitioner puts in their best effort to cultivate virtues, meditation, and wisdom (as mentioned from my previous post here