If you're being a purist, then you're in good company.
I don't have the references to hand here at school, but Jerome Kern complained that no one heard his songs performed properly unless they saw his musicals in the theatre. He generally hated dance-band, live radio, and recorded interpretations of most of his songs because of the way the arrangements changed what he had written.
Meanwhile, Richard Rodgers - I believe in his autobiography,
Musical Stages - maintained that he wanted his songs sung strictly in rhythm as he composed them, and he particularly opposed the practice of back-phrasing.
If you're working with students in a classroom setting, you could use the power of the gradebook, and indicate that students who indulge in copying other performers' specific inflections will be graded down on their performances. If we're talking about students performing in an ungraded extracurricular production, you could indicate that you're unlikely to cast such students again in the future (if you have enough castable students to be able to follow through on such a statement). At the same time, it seems a pity to resort to punitive measures in performing-arts instruction when what you're really trying to do is set your students free as interpreters.
I say keep fighting the good fight, urging your students to work from the text rather than from YouTube, etc., and to be original in their interpretations. You might not convince every one of them, especially not now, but some will get your message and flourish, and others will realize later on the truth of what you've taught. I remember with great embarrassment my own hubris back in high school, when I sometimes foolishly thought that I knew more (or better) than some of my teachers! If only I could apologize to some of them today ...
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Jeff Grove
Theatre Teacher, Aesthetics Department Chair
Stanton College Preparatory School
Jacksonville FL
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