I'm puzzled by that reaction. In my head at least, the distinction is pretty deep, and describing The Economist as "libertarian" in any sense would be clearly misplaced, other than to say it sometimes supports positions libertarians also agree with.
Historically, when The Economist was founded, libertarianism would have been associated with French anarchism. The core, consistent theme of libertarianism is that individual rights trump arbitrary interference by a collective. The various forms of anarchism are sort of natural "extreme" forms of libertarianism. Intellectually, libertarianism starts with a negative claim that except in extraordinary cases, the collective has no right to interfere with individuals. This remains true today. Core items (legalization of prostitution, drugs, elimination of many taxes) begin with the pretext that the collective has no right to regulate individual behavior in these domains.
Classical liberalism emerged in Britain (Locke, Smith, Mill, etc.). It has roots in a blend of English utilitarianism and enlightenment-era attempt to root the form of government in reason. "Rights" in classical liberalism are important, but they aren't necessarily more foundational than well-being. Anarchism is seem as trivially untenable (Hobbes' "nature red of tooth and claw"). Liberalism tries to identify a core set of functions (security, laws and their enforcement, public infrastructure) and a set of mechanisms (constitutions, elections, courts, etc.) to implement them, and has a very enlightenment-era emphasis on building institutions that are robust to "bad" actors. It does cleave towards a minimalist view of government, and does elevate rights like freedom of speech, but these are seen as intrinsically grey and are framed much more in terms of limiting the power of government institutions to ensure that they remain true to their mission/function.
I don't think that's flame bait, or super controversial.
Do the words mean something else to you?