The public that gathered on 19 December, 1890, at the Maryinsky Theatre in Saint Petersburg gave Tchaikovsky's The Queen Of Spades a very warm reception. (source)
I'm investigating the senses of the term the public and the reasons why it seems to always take the definite article or other determiner, such as the possessive pronoun my. I got interested after reading this question at ELL.
I have the hunch that the use of the public in the quoted sentence is wrong somehow, and the members of the public would've been a better choice. It seems to me that the public is too broad a concept in English to stand for "the group of people gathered in a particular place at a particular time".
Am I right? To a native speaker, would the mention of the public seem out of place in the specific situation described in the sentence?
(Such use is okay in Russian)