I'm not a lawyer, but my job includes looking after the corporate reputation for a big FTSE company, and have spent 20-odd years doing similar roles for FTSE companies, most of them household names.
Over the years, we've had various people claiming mad conspiracies, setting up websites claiming we do awful things etc, scammers using the company name for 'lotteries' and fake employment etc.
We have never sued or even attempted to sue any of these people, and they are deliberately trying to damage the company reputation.
I can't see any mechanism by which the company could sue, let alone the PR nightmare that would be any sort of 'David v Goliath' lawsuit.
So from the perspective of my role in a company, it would never happen.
To give you some examples of the sort of things we deal with in a typical year... we've had investors who have lost money buying our shares set up blogs claiming all sorts of weird financial mismanagement, and we usually ignore them on the basis they will have very few visitors. We don't even bother engaging with the individual
In one company I worked for, we had someone set up a website called 'CompanyXkillspeople.com' which was making all sorts of lurid claims, and we sent the host a legal letter to get it taken down, but I don't think we even properly investigated who was making the claims.
We fairly often get disgruntled people threatening to 'go to the press' unless we resolve their issue, give them compensation for a past issue, and occasionally, it will be something like sack their cheating ex husband.
99% of them don't know how to contact 'the press', and the very few that do usually result in a journo we know quite well telling us over lunch that they've had a weird email from a very angry person.
This would be pretty standard across any sort of large company, especially if they are 'customer facing' in any way - a retailer, utility company, etc
Happy to DM you more context or insight into how a company would typically handle a reputational issue, if it would be helpful