The only requirement is a sound argument. The source is an unimportant detail.
For example, the more CNN reported about COVID and Vaccines, the less likely the already vaccine hesitant were to get one.
Obviously for contentious topics you need to modulate this based on how politicized it is and which media outlet is reporting the negative stories about Twitter, or whichever topic some side has an agenda against. In this case, the people who are fans of Musk are almost exclusively people who oppose the outlets that have been posting negative stories about Twitter.
If Fox News, NYPost, or CoinMarketCap were posting negative stories about Twitter, then GP may have a point - the stories would eventually inflict damage to the brand. But as it stands today, the only outlets crusading against Twitter are the same outlets fervently opposed by most Twitter supporters, so the negative coverage will only make Twitter more endearing to them. Anyone more agreeable to those outlets probably already dislikes Twitter/Musk, so the negative branding effect will be mostly negligible.