The generic payment warning debit emails are just that ... generic. When you entered the routing & account numbers in the program the processing bank doesn't know what type of account it is since checking accts, savings accts, broker's accounts with check writing privilege's and pre paid debit cards all use the same routing/account numbers formats so in the TT system they are all the same.
That said ... even if your bank said the debit could not happen from a savings account I would not count on it ... although paying bills from a savings account is highly discouraged by virtue of limits and fees that are imposed they are not forbidden so your sweeping statement is not the entire truth for all banks.
