True, according to usa.gov:

How to get dual citizenship or nationality

Having dual citizenship, also known as dual nationality, means being a citizen of the United States and another country at the same time.

Learn about the requirements for dual citizenship

Whether you were born an American citizen or became one through naturalization, if you have dual citizenship, you:

• Owe allegiance to both the U.S. and a foreign country
• Must use a U.S. passport to enter and leave the U.S.
• Do not have to choose one nationality over the other. As a U.S. citizen, you may naturalize in another country without risking your U.S. citizenship.

Learn more about dual citizenship or nationality.

Get dual citizenship

Your eligibility to become a dual citizen depends on the policies of the second country where you are applying for citizenship.

Dual citizenship if you are a U.S. citizen

If you are a U.S. citizen who is seeking dual citizenship, you must find out if the other country recognizes dual citizenship with the United States.

Contact the other country's embassy or consulate to learn if you are eligible.

Dual citizenship if you are a citizen of another country

Some countries allow people to keep their citizenship after becoming U.S. citizens, while others do not.

Contact the other country’s embassy or consulate to find out if they recognize dual U.S. citizenship.

If you qualify for dual citizenship, you must first immigrate to the U.S. Then you must become a permanent U.S. resident before being eligible for U.S. citizenship. 

Learn more about immigrating to the U.S. And find out how to become a permanent resident.

The US will only recognize them as American citizens but that doesn’t have any bearing on their citizenship elsewhere. There’s nothing in the US that would give you something different or extra if you have citizenship elsewhere so it doesn’t make any difference. The US can see you’re an American/French or American/Indian or American/Nigerian but only care about the American part, you being that other thing is irrelevant to the government. So they only “recognize” the US because it’s the only part relevant to the state, they don’t make you renounce anything or anything like that. You can absolutely be a dual, or more, citizen but the US government only recognizes the one it cares about, its own.