Should you show your current company an offer letter?

I would preferably like to stay at my current company for the right price but have received an offer else where for almost 17k higher. I thought I did the decent thing by telling them first instead of just accepting without negotiating or giving them a chance to match first. 3 other of my team members left in the span of just 2 months and they LITERALLY can't afford to lose anyone else.

I never thought they'd ask for a copy of another company's offer letter because it wasn't ethical. Has anyone experienced this? I don't plan on giving them a copy of it, the distrust doesn't sit well with me.

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