The taxpayer qualifies for the Married Filing Separate filing status. Thus your reference to the phrase: "and you do not qualify for another filing status" is not relevant.
Pub 17, page 20:
The phrase "you do not qualify for another filing status" is referring to a taxpayer who was unmarried or legally separated from his/her spouse. As such, Married Filing Joint and Married Filing Separate are not allowed. The other two options besides single are Head of Household or Qualifying Widow(er). Thus, if a single person cannot file as HOH or QW, then single is the only other option.
Nothing in that implies that someone who can file as MFS has the option to elect to file as single.