ίδιος = same
Very can be translated in many ways in Greek, but 'ίδιος' does not work... If you explain how you reached this conclusion maybe we can clarify correct usage further.
Please check the examples here http://www.wordreference.com/engr/very. For "The very mention of his ex-wife caused problems." you could potentially say 'Η ίδια η αναφορά...' but it wouldn't be accurate enough and it's rather poor in my opinion.
Seems to me I've even seen examples here on Duolingo, though I don't think I have access to past examples here. Glosbe gives, "by the very persons making the request" as "από τους ίδιους τους αιτούντες"; and "the very person making the confession" as "το ίδιο ακριβώς πρόσωπο που...." When you think about, "the very guard who locked me in" essentially does mean "the same guard...," right?
A computer-generated translation can only do so much. You're correct that "the very guard" = "the same guard" but it's somewhat archaic, though one can still hear it at times, esp. probably in England. That use of very is common in Shakespeare. For instance, in All's Well that Ends Well at 3.6, "when his disguise and he is parted, tell me what a sprat you shall find him; which you shall see this very night." IMO, "the very guard" is just too archaic for DL to go out of their way to put it in as optional. But I wouldn't fall on my sword over it.