As other answers have noted, since 1990, the Department of State has had an administrative presumption that applies to some (but not all) of the potentially expatriating acts. It applies to 8 USC 1481(a)(1), (2), (3), and (4), but not (5), (6), (7). It presumes that someone who performs these acts do not intend to relinquish citizenship unless they affirmatively assert the intention.
You might also wonder what happens without the presumption (e.g. before 1990 when the presumption was established, or for the potentially expatriating acts that the presumption does not apply to). The US Supreme Court decision in Afroyim v. Rusk (1967) ruled that it was unconstitutional for a US citizen who was born or naturalized in the US (within the meaning of the Citizenship Clause of the 14th amendment) to lose US citizenship under any circumstances unless they intended to relinquish it. (Except for fraud in naturalization which is not considered loss of citizenship since the person is considered to have never been a citizen.)
The US Supreme Court decision in Vance v. Terrazas (1980) further reinforced the Afroyim decision, ruling that the intention to relinquish citizenship must be proven separately from the performance of the potentially expatriating act, and the act cannot be taken as conclusive evidence of the intent. At the time of the Terrazas decision, the statute did not require intention to relinquish (this was added in 1986), but it did contain the provision that the claim must be proven by "a preponderance of the evidence". The Supreme Court in the Terrazas decision ruled that this means that the intention to relinquish must be proven by "a preponderance of the evidence". (They also ruled that "a preponderance of the evidence" is an acceptable standard, and that it did not need to be "clear an convincing evidence".)
- In establishing loss of citizenship, the Government must prove an intent to surrender United States citizenship, not just the voluntary
commission of an expatriating act such as swearing allegiance to a
foreign nation. Congress does not have any general power to take away
an American citizen's citizenship without his "assent," which means an
intent to relinquish citizenship, whether the intent is expressed in
words or is found as a fair inference from his conduct. The
expatriating acts specified in § 349(a) cannot be treated as
conclusive evidence of the indispensable voluntary assent of the
citizen. The trier of fact must, in the end, conclude that the citizen
not only voluntarily committed the expatriating act prescribed in the
statute, but also intended to relinquish his citizenship. Cf. Afroyim
v. Rusk, 387 U. S. 253. Pp. 444 U. S. 258-263.
- Nor is the presumption of voluntariness provided in § 349(c) constitutionally infirm. While the statute provides that any of the
statutory expatriating acts, if proved, is presumed to have been
committed voluntarily, it does not also direct a presumption that the
act has been performed with the intent to relinquish United States
citizenship, which matter remains the burden of the party claiming
expatriation to prove by a preponderance of the evidence. [...]
The case of Terrazas might also have parallels to your question. He had both US and Mexican citizenships at birth, but in order to obtain a certificate of Mexican nationality, he had to sign a statement renouncing US citizenship. He also made conflicting statements to US consular officials regarding his intention to relinquish in the years afterwards. The US decided that he lost US citizenship, and it went to court. After the Supreme Court decision, they remanded the case back to the lower courts to determine whether he had the intention to relinquish by "a preponderance of the evidence", and the lower courts ruled that he had, and that he lost US citizenship. So making a statement to a foreign country to renounce US citizenship (although in Terrazas's case it was to obtain a certificate rather than to obtain citizenship itself) did cause loss of US citizenship under that standard for Terrazas. But it was not based on the fact of the statement alone, but based on "a preponderance of the evidence" in his situation.