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.
The second, more structural reason is a common theme with brand equity, you can do a lot of things over time to damage a brand and non of them invididually will sink your company. But these shots to the company accumulate, and eventually it's gone too far to come back from, you can't recover. To a certain extent you saw this with digg, the redesign was the obvious exodus point, but the trust had been lost far earlier - people were ready to walk away.
In the same way, Twitter doesn't look today like it's collapsing, but it's done a lot of permanent damage to itself. That broad base of quirky and interesting people you used to follow on twitter? They're not there anymore, they don't want to be on that weird homophobic guy's platform. Some of the people have stayed, but those communities largely exist on other platforms now, Twitter is no longer the centre of gravity. But those aren't the thing making twitter a billion dollar platform. The platform is still busy, but it's full of crypto bros and VC influencers, people who will take great pride in telling you how AI is going to make <person with high social status> unemployed. But that's not a healthy ecosystem - those are the guys who move in to try and farm social capital from the high status individuals, but the high status individuals aren't there anymore - a deliberate move from Elon. So yeah, it's still alive, but to some extent the value has already walked out the door. There hasn't been the big bang to crystalize this yet, but it seems highly likely that Twitter has given up its space as a cultural centre-peice. The cool kids have moved on.