One possible solution is to include a tooltip or some other notice on the forum formatting interface that quoting doesn't ping.
Another idea is to automatically insert a ping to the user when the "Quote" button is clicked. For example, if I clicked quote on one of my own posts, the comment box would be pre-filled with this, rather than just the quotation itself.
[quote=Duke said]Hello![/quote]
@Duke
@Duke
This way, a user can intuitively be shown that the [ quote ] code itself doesn't ping, and can just delete the ping if pinging is not their intention.
A separate issue is pings that are edited into or removed from a post. It might be useful to have another notice when a user clicks "Edit" that any pings they add or delete will not be accurately reflected in notifications.