It is an interesting topic, In my experience, the problem is not so much the opening of the account, but after opening the account and the funds that reach the account match what you said when opening the account. Of course that depends on what amounts we are talking about.
It is really tempting not to give all the details about your source of wealth, but it is also good to keep in mind that if you intend to regularly deposit into this same account, this can be a problem if the bank starts asking questions about these deposits and they do not match what you originally stated.
If you decide not to tell the whole truth, it is important to structure all your fund movements before you get them to the account so that you can always justify the incoming funds based on what you have declared originally. Is not always easy.
Transferred all its source of wealth to a single bank without telling the whole truth is in my opinion unconscious and can quickly turn into a nightmare for large amounts.
Sometimes it is better to visit several banks until you find the one that accepts you in relation to your commercial activity, you sleep more quietly. Or another option is to distribute the funds to several banks not to sound the famous alerts : -) And nobody will ask questions in this case.
@Martin Everson, I think I do not have to deal with good banks or not choose the right countries because to report a 7-digit amount as savings, most of the banks that I have dealt with will ask how that amount was generated.. Even by declaring the sale of real estate, some banks ask how the funds that enabled the purchase of these properties were generated.
That is the real problem and dilemma when we have activities considered risky by most banks.