Acting in a disreputable way while wearing clothing that represents my company could get me fired, but that doesn't make the local supermarket an extension of my workplace just because I walk in there with a company shirt.
Which is, metaphorically, what happened here: when using the company account you're not a private citizen in a t-shirt with a logo; you are the company.
Yep, I /totally/ agree with you. Still doesn't make LinkedIn an extension of the workplace.
Please think about what that means for at least one second. For most software engineers, if LinkedIn is an extension of the workplace, then by the wording of their employment contract (which invariably includes IP ownership clauses for everything done in their capacity as an employee), their employer owns all their content on LinkedIn, and could request it any time.
That potentially makes it very hard for software engineers to use LinkedIn on a private account to look for a new job without their boss knowing.
Absolutely no-one has expressed a desire to lay claim to your personal LinkedIn account. If you continue to argue that this is about personal rather than company accounts, I will interpret as a sign of explicit bad faith on your part.