I am not sure why they seem idiomatic to me, and hope someone else will take an articulated position on the issue.
Turning the question around, however, can you explain why they are merely sum of parts?
As a check, see also give back at OneLook Dictionary Search and buy back at OneLook Dictionary Search. --Dan Polansky 08:16, 26 November 2009 (UTC)
I have added the somewhat cliched karmic feel-good sense to give back. My McGraw-Hill's Dictionary of American Idioms and Phrasal Verbs, edited by Richard Spears, 2004 contains both, as do some other OneLook sources. Mostly the includers rely on Wordnet, generally the most inclusive of references there. They both seem like phrasal verbs to me, but I have previously relied on Algrif's informed and experienced judgment for hard cases. DCDuringTALK 11:05, 26 November 2009 (UTC)
What possibly gives me the impression of idiomacity is that the direct Czech analogue of "give back" - "dát zpět" - is much less common than "vrátit" - an analogue of "return". So when I come to English from the Czech background, the construction to "give back" in the sense "to return a borrowed item" seems peculiar to English, hence idiomatic. But I admit that the term may seem sum-of-parts from the native point of view.
Another term that I would like to see included in Wiktionary - strike back - is also included only in non-mainstream dictionaries: strike back at OneLook Dictionary Search; also hold back in the sense "to prevent" - "What holds you back from doing it?" - "What prevents you from doing it?".
What I am saying with these in part digressive remarks is that, from my point of view, the "* back" verb constructions look usually like phrasal verbs rather than mere sums of parts that require no explanation and example sentences for the full grasp of their native-sounding use. --Dan Polansky 09:18, 27 November 2009 (UTC)
As to buy back, if there were context tags, finance for the especially clause of the first sense, in line with the 4 OneLook business glossaries that have it, and bartending for the other (unattested) sense, would we challenge it? DCDuringTALK 11:15, 26 November 2009 (UTC)
In my opinion, which seems to be supported by most dictionaries, the "back" phrasal verbs need to be treated with caution. If you cannot find another meaning other than "return", then it should not be treated as a phrasal verb, which is the case we have here with buy back. I cannot find any dictionary that includes this entry, but let's see if anyone cares to differ. -- ALGRIFtalk 13:53, 26 November 2009 (UTC)
While mainstream dictionaries such as M-W don't include "give back", there are online dictionaries that do so: give back at OneLook Dictionary Search, including Encarta® World English Dictionary, North American Edition and WordNet 1.7 Vocabulary Helper. --Dan Polansky 09:18, 27 November 2009 (UTC)