I don¡¯t necessarily see this as a problem. Over here in France, and I think it¡¯s the same within the EU, once the money is in your bank account, there is no way for anyone but yourself to withdraw it without a court order.
No one can have access to anything on any of your bank account(s) without a court order, with the exception of the IRS who can take anything they want without warning if you haven¡¯t paid your taxes.
My PayPal account has been linked to my bank account for years and years, and I¡¯ve never had any problems so far.