Glass cut into small piece of tire near sidewall?

Hello, On my tires I was worried that I cut an area on the Shoulder with a piece of glass. I heard that cuts to the shoulder and sidewall mean replace the tire, even if it isn't leaking air. Is this true? I don't think the cut is too deep and the Shoulder is an area that is right between the tread and... show more Hello,

On my tires I was worried that I cut an area on the Shoulder with a piece of glass. I heard that cuts to the shoulder and sidewall mean replace the tire, even if it isn't leaking air. Is this true?

I don't think the cut is too deep and the Shoulder is an area that is right between the tread and sidewall...
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