Yes it's possible. Just like all other immigration applications; study visa, vacation, medical etc, embassies/consulates/visa offices routinely write to banks and other financial institutions to verify the authenticity of bank account statements which people use to support their visa applications, FSW inclusive.
Having worked with a major bank's Audit and Inspection Unit, I can confirm to you that banks respond to the embassies wether the statements are real or fake and in some cases, try to prosecute those who use the bank's name to perpetrate bank fraud. Banks don't find it funny when their letter heads and statement paper is used for fake POF.
Like I stated before however, this verification is random and based on if the VO has doubts on the financial capacity of any applicant. Some people will not be verified, some people can not escape bank document verification, cheers.
