It wasn't a stupid thing to do. The other company should have respected your confidentiality; its their fault, not yours.
I've been in a similar situation before. In my experience, I found it gave me the opportunity to dicsuss with the brass of the company what I thought was wrong. If they know and you're crucial to the company they'll be willing to listen. They won't like it, but they will listen.
When it happened to me, they did try to change, but I just found it too little, too late, and ended up leaving anyway. It turned out for the better because I got a really good offer somewhere else.
I wish you luck.
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