Contemporary artists and museums: the record

[Seriy]

Under such a complicated name I would have wanted to touch on a delicate topic that everyone knows but rarely speak.
 In the CV of a living artist is important to mention all sorts of museums - private, municipal, regional, state and world in which stored its work.
 How can I verify this information? and how to understand this information?
 Several recent cases in which I tried to check on the discovery site of the museum world by his search for the artist's name, mentioning that the collection of this museum is its work resulted in a response-not in the list, an artist museum does not know.
I am not sure that the artist is all misinformed. Rather, the meaning of the phrase - work is in museum collections - may have a different filling.
 At a forum of experienced collectors and museum professionals, can they kindly give an explanation?
  Here the artist gave the museum work, whether it is the inclusion in the collection? or such work was not considered a collection? It always takes the work of the museum as a gift?
That museum has handed over its facilities for commercial exhibition. And the artist writes, Tretyakov Gallery, evaluated and held an exhibition. That is, if the show was a commercial, does the artist the right to use the name of the museum?

 Grateful for any suggestions and explanations.