This is partially inaccurate, and entirely needing clarification. The statement is correct that under the MFN rule, WTO members are generally required to apply the same tariffs (and other trade rules) to the products of all WTO members. This means that if a country grants a favorable tariff rate (the “lowest tariffs”) to one member, it must extend the same rate to all other WTO members. This principle is aimed at preventing discrimination between trading partners.
The MFN rule does allow for certain exceptions, including entering into FTAs (Free Trade Agreements) or “customs unions”, where they apply lower tariffs to members of these agreements without extending the same treatment to all other WTO members.
There are also special preferences regarding developing countries, which allows developed countries to apply lower tariffs on goods from developing countries without violating the MFN rule.
The claim that “WTO members can charge higher tariffs if they apply these nonreciprocal tariffs to all countries” is incorrect. The MFN rule does not permit charging higher tariffs across the board simply as long as they are applied to all countries. In fact, the WTO agreements limit tariff rates (known as “bound tariffs”) that countries can impose. Members can raise tariffs only if the tariffs remain within these negotiated bound rates or if they have a legitimate reason, such as invoking safeguard measures (to protect a domestic industry) or through an authorized dispute settlement process.
Full contextual analysis of Section 4.6: Trade here.