This is quite blatant not true. Probing will show nothing in terms of privacy. As I explained in this guide you can use private channels/ private nodes / keysend in a simple mode that cannot be traced in any way. Use your imagination, there are many ways to do it.
I'm sorry but you're wrong, especially in your generous use of extreme statements such as "show nothing", "any way", and "full privacy". Not only is probing a privacy concern for public channels but it's a concern for these "unannounced" channels you think are private as well. It's in my linked guide above, give that a read and let me know if you have any questions.
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