Again I don't know how this works in USA but in Europe it is now same all over the place. The bank is required to be able to identify you in person, and update your information regularly. One of the items they need to know is all the countries you are taxable. They are then required to offer this information to the tax authorities in the bank's own country.
The tax man then shares the information with all the countries the bank reported. They will give out your name, tax ID, bank name and account number as well as the balance in that account. This will be done automatically with the CRS end of every year.
This is certainly not true in Europe. On the contrary if the bank doesn't keep it's customer information up to date and offer that information to the tax authorities they face penalties and in worst case revoking their banking license.
I am pretty sure that's what they want us to believe.
If by offshore you mean in a country that will not provide the information to other countries then you are absolutely correct. However those countries are now few and even they are being pressured to join the agreements. And as soon as you move your money away from them to any other country they will require you to report what is that money and where did it appear.