Italian copyright law protects works regardless of whether they have been "fixed" (a condition that the Berne convention permits its signatories to impose but does not require). In addition to this, EU directive 2001/29/EC requires member states to grant performers "the exclusive right to authorise or prohibit direct or indirect, temporary or permanent reproduction by any means and in any form, in whole or in part ... of fixations of their performances."
Therefore, the crowd member's posting of the video without the performer's permission was an infringement of her rights both as a performer and as the author of the musical work.
Even in a jurisdiction such as the United States that requires fixation as a condition for the existence of copyright, the copyright accrues to the author of the work, not to the person who fixed the work. Had this event occurred in the US, the crowd member's recording the songwriter's performance would have caused the songwriter's copyright in the song to come into being, and the subsequent posting of the video would still have been an infringement. At least, this is the natural conclusion from the literal provisions of the statute; I do not know whether courts have interpreted it differently. The statute, 17 USC 102, says
(a) Copyright protection subsists, in accordance with this title, in original works of authorship fixed in any tangible medium of expression, now known or later developed, from which they can be perceived, reproduced, or otherwise communicated, either directly or with the aid of a machine or device. Works of authorship include the following categories:
...
(2) musical works, including any accompanying words;
Beyond the requirement to be in a "tangible medium," there is no limitation on the circumstances of the fixation.