I've heard of this too. This talks a bit more about it
https://travel.state.gov/content/travel/en/legal/travel-lega... and also
https://travel.state.gov/content/travel/en/legal/travel-lega... that mentions more different ways.
For some cases it sounds like only if you have the intention of giving up your citizenship, then you have to get a "Certificate of Loss of Nationality". But I'm not a expert in this area, but I can see where this idea is coming from.
Such employment, however, will result in one's
expatriation only if done voluntarily with the intention
of relinquishing U.S. citizenship. Running for foreign
office, even foreign head of state, is not a potentially
expatriating act; only accepting, serving in, or
performing the duties of a foreign office are potentially
expatriating as described above.
The Department has adopted an administrative presumption
that U.S. nationals intend to retain their U.S.
citizenship when they naturalize as nationals of a
foreign state, declare their allegiance to a foreign
state, or accept non-policy level employment with a
foreign government.
Also:
The presumption that a person intends to retain U.S. nationality is not applicable when the individual:
1. formally renounces U.S. nationality before a consular officer;
2. serves as an officer in the armed forces of a foreign state engaged in hostilities with the United States; or
3. takes a policy level position in a foreign state
Cases in categories 2 and 3 will be developed carefully by a U.S. consular officer to ascertain the individual's intent toward U.S. nationality.
Kinda confusing, but sounds like if you were elected prime minister of Canada (which would be policy level), then there's the presumption you wanted to give up citizenship, while working as a employee for the Canadian government such as driving the snow plows would be ok but things are reviewed by case by case.