How to check one of multiple checkbox group listed in on PDCheckbox field?

Using PDFBox 2.0.8 for the first time on PDF files I don't have any control over. Cycling through the form fields I get this output for one of the fields.

field = Check Box5{type: PDCheckBox value: COSName{}}
field.getFullyQualifiedName() = Check Box5
field.getFieldType() = Btn

The actual field on the PDF is an option of choosing one of 4 options ('CheckBox Group' if you will?). Call them A, B, C, D. So the end user experience is that if i choose C it unchecks A.

When I do the following:

if(field.getFullyQualifiedName().equals("Check Box5")){
  PDCheckBox checkBox = (PDCheckBox) field;
  checkBox.check();
}

It checks 'A' as expected (sort of), but subsequent check()s do not make any difference. How does one choose 'C'?

EDITS:

1. Actual PDF Downloaded Here.