Actually “may” would be more accurate to the reality of how this gets applied in the real world. While accepting citizenship in another country could technically by implication, be interpreted to be a clear demonstration of the desire to relinquish US citizenship, it isn’t necessarily the case.
Mainly though there just isn’t any protocol between countries to compare notes on who has been accepted as a citizen to make sure they revoke their citizenship in their country of origin. A US citizen might move to Italy, marry an Italian, apply for citizenship, and be granted Italian citizenship. At that point nobody in the US State Department would be aware of this happening. There is no obligation on their part to formally relinquish their US citizenship with the US when accepting another citizenship. There is no obligation on the Italian government to notify anyone they have welcomed a new citizen, and there is no obligation on the US government’s part to check with each country daily about any US citizens who have applied for nationality over there. Some day this person might get divorced, decide they want to go ‘home’ and make the argument, if one were necessary, that it is the land where they were born and they have a right to return.
There are plenty of US citizens that hold multiple citizenship with other countries due to marriages, parents, etc. but have no intention or desire to relinquish their natural born US citizenship. So, if pressed on it by the State Department they would say “No, I never meant to stop being a US citizen. That is where I was born. Duh.”, and that’s that. It might create some ripples with their citizenship in the new country, where they probably had to swear off loyalty to any other country, but that won’t affect their US citizenship, and again that would only be so if there were some protocol in place for their new country to be notified about it, which there isn’t.
From a few quick searches, multiple-citizenship is fairly common, fears are frequently expressed on forums about loss of US citizenship as a result and the resounding answer seems to be there have been very few, if any, cases of the government revoking citizenship from a natural-born citizen who ultimately did not want it to be revoked and fought it.
It is frequently argued that even people who *did *want their citizenship revoked and petitioned the State Department, going through the specific procedure and loads of red tape in order to officially renounce their US citizenship, were still able to come back later by saying basically “Whoops. I know what I said, but this is the country of my birth. You can’t deny me citizenship even though I said I wanted you to at one time”.