That may be Bangkok Bank's (or that particular location) policy, but that doesn't make it the policy of all Thai banks, or even other Bangkok Bank branches.
The advice often given to foreigners, even those visa exempt or tourist visa, is to keep trying the different branches until you find one that will open an account. Likewise, several agencies offer assistance in opening a Thai bank account.
The Pattaya City Expats Club has this comment on their webpages about banking in Thailand:
bravo19
To obtain an OA visa, you must apply at a Thai Embassy/Consulate in your country of residence, it is not available from Thai Immigration. To obtain a Non-O from Thai Immigration, you need to show you have 800k baht in a Thai bank OR, if using monthly income, a Monthly Income verification from your Embassy (such verification is not available for holders of passports from Australia, UK, USA, & now Canada). Once you have a Non-O Visa, you can use Thai bank passbook/statements to show monthly deposits from a foreign source of at least 65k baht to get an annual extension of the permission to stay.