The meaning of Bhagavan is as follows.
The Sanskrit word bhagavan is explained by the great authority Parasara Muni, the father of Vyasadeva. The Supreme Personality who possesses all riches, all strength, all fame, all beauty, all knowledge and all renunciation is called Bhagavan.
There are many persons on earth who are very rich, very powerful, very beautiful, very famous, very learned, and very much detached, but no one can claim that he possesses all riches, all strength, etc., entirely.
Visnu Purana (6.5.72--75,79), defines Bhagavan thus:
"O Maitreya, the word bhagavan may be defined as a name of the Supreme Brahman, who is pure, free from all material contamination, full of unlimited powers and opulences, and the original cause of all causes."
"O sage, in the word bhagavän, the syllable bha stands for the word bhartä, which means the maintainer of everything, or the shelter upon whom everything rests, and the syllable ga stands for gamayitä, the leader of everyone, or the creator and annihilator of the entire cosmic manifestation."
"The name bhagavan stands for that Supreme Person who is full in the six opulences (bhaga) of all wealth, strength, fame, beauty, knowledge and renunciation."
"In the word bhagavan, the syllable va stands for the verb vas (to reside), because He is the Supreme Personality of Godhead in whom the entire creation rests, and also because He is the Supersoul, who remains in the hearts of all conditioned souls. The syllable va also stands for the word avyaya (unchanging), which indicates that the Supreme Person is eternally the same."
"In this way the name bhagavan means that person who posesses all strength, knowledge, beauty, fame, wealth and renunciation, and all other auspicious qualities, and is also completely free from any fault or defect."
Since the baba in question does not possess the above mentioned six opulences, he is not Bhagavan.