Yup, that's right. As a precaution, one thing to do may be to inform the immigration officer while exiting and re-entry that you are on a multiple re-entry permit. If they do not realise it by any chance, they may treat you as being on a regular single entry tourist visa and then your previous valid visa may get automatically cancelled.
I had my BB account frozen, went into the branch and provided copies of my condo contract, valid visa and Thai driving licence. Waited a week. Meanwhile had to go change some Forex to pay rent and expenses. Opened an account in KBank to help with daily QR/Truemoney payments. Went back to the branch to ask why the delay. It turned out that they had not taken or, perhaps, misplaced my condo contract copy. That was done on the spot and 15 minutes later the account was working again. Tbh, both times the staff were nice and polite. It's not that Thailand does not "want foreigners". Just be on a proper visa for opening a bank account. In my opinion, the surge in scams over the last couple of years has led to an "unsafe" perception, leading to a significant drop in Chinese tourists (highest tourist revenue) and there was a need to clean up.