The couple shut themselves away

[Guest]

Test No. incompl/inter-10 "Close/Shut", question 8

After the terrible experiences that they had been through, the couple ......... themselves away from the community.

(a) shut
(b) shuts
(c) closes
(d) closing

Test No. incompl/inter-10 "Close/Shut", answer 8

After the terrible experiences that they had been through, the couple shut themselves away from the community.

Correct answer: (a) shut

Your answer was: incorrect
After the terrible experiences that they had been through, the couple closes themselves away from the community.
_________________________

why is closes incorrect?

[Alan]

It couldn't possibly be closes because the subject is they and the expression shut yourself away from means remove yourself from society and not talk to anybody.
_________________
English as a Second Language
You can read my ESL story Phrasal Verbs/bring

[Casafon]

I think the difference between close and shut is that
shut has more the sense of "separation or complete isolation from the outside", it is quantitive (complete) and qualitative (spearation) different from close.
Is that correct Alan?
Thank you in advance for answering