I don't believe this at all. First off Max Mara's atelier is in Italy, Balenciaga's in Paris. No way in heck can that coat go to Italy and back without Balenciaga demanding it's where abouts. Secondly no one lends out samples for 24 hours. That's crazy. A fashion closet needs time to get the samples, check them in, tell the editor they have arrived, and then the editor looks over the samples, and then 92% of the time on a different day the editor shoots the samples. A fashion house or pr firm is lucky to get clothes back in a week. Balenciaga has the clout to demand three days, but a day, it's just ludicrous. You can't do a high budget on location shoot with 24 hour samples, and most Vogue Paris shoots are that way. Lastly I highly doubt Carine would personally send the coat, especially a sample. If she really wanted to give Max Mara a Balenciaga coat it wouldn't be a piece that has to be returned to Balenciaga. Especially if Max Mara wants to truly study the piece they would take it apart.
The most I could get out of this rumor is an intern (cause they return garments, not editors) accidentally put a Balenciaga coat in the wrong bag, and Max Mara got it. Obviously Balenciaga would be pissed that their coat went missing. However these mistakes happen all the time and it's nothing to ban a magazine over.
edit: My money goes towards the Sauve rumor. However, I'll doubt anyone except VP and Balenciaga will ever get more details than what has already been said.