Connect support chats are being created by "Guest" users.
Connect support page is a public page and non-authenticated users can create chat queue records in your instance. To verify the same, access the following link without logging into the instance(In an incognito window).
So even if a user was logged out of the instance, they can still create chat records as guest users.
To make sure the users are logged in when creating a chat record, you need to make sure $chat_support is not a public page. For that please set active False for the following record.