Are they confusing the New/Unread Items Indicator (located on Content Navigation Tabs) with the Alert Count Indicator (located on the Alerts Link)? This is a common mistake that a very large number of people make. New Content Indicators are NOT "alerts" (they are not even remotely connected).
If that is the case, the New/Unread Items Indicator can be Globally Disabled via Showcase options. Users also have the ability to enabled/disable this as well in their Browsing Preferences settings (as shown below)
Alert Preferences are ONLY for ALERTS (they don't effect the New Items Indicators on Navigation Tabs for any addon).
NOTE: Alerts for NEW Showcase Items are ONLY sent out when WATCHING A CATEGORY.
Alert Preferences also do not effect Alerts set for WATCHED CATEGORIES. Each Watched Category has its OWN preferences (so that you can watch Category A, G, X and get alerts for them and watch category Z, J, K and not get alerts from them, but get emails instead.
As you can see in the below image, this category is set to send alerts when new items are created for it and any of its sub categories.
My guess is that they are either talking about the New Items indicator (which is not an alert) or they are watching Categories and having Alerts sent for those categories when new showcase items are created.