ok. Here is another perspective to see logic from that may help : slots.
An answer has a slot in which you can fill in.
A true/false dichotomy is binary and there is only one slot available to fill.
A true/false question can be reconstructed to allow for A or B answers instead.
You can also have C. It is a slot. You can fill that slot in with anything that fits.
I can answer “I don’t know” to a true/false. That is not wrong : it is an answer that fits into a slot.
The examiner asking the question may decide that they do not like the answer given due to a set of rules the examiner is using to determine a state of correctness.