In investigating the claim "Doubts over U.S.-EU intel sharing are pushing European agencies to strengthen cooperation." This claim comes from a trustable news magazine called "POLITICO", which has been working since 2007 worldwide. Regardless, that the intelligence and security officials were anonymous, they still talk to people involved in the intelligence agencies in Europe.
Furthermore, the source provided by the fact-check explains their reasoning in a logical manner, saying that from current events in the U.S. with Trump administration stopping sharing of battlefield intelligence with Kyiv (capital city of Ukraine), it shows support towards Russia, when Russia has been non-stoping attacking and invading Ukraine, it has become harder to fully trust United States.
The cooperation between EU and North Atlantic Treaty Organization (NATO) has deepened because of the war Russia started with Ukraine. Therefore, United States showing no interest or sharing of intelligence in order to stop the war is the reason why European countries do not trust U.S. as much as they did before, European countries leaning more in each other.
The NATO cooperation being explained by the European parliament in an official website link finishing in ".eu". Which main goal is to share cyber security/information to remain in peace with Europe and U.S..
While searching for other sources of information, I found the news magazine "The Cipher Brief" backing up the POLITICO sources, and reaching to the same conclusion. Therefore, even though this fact-check is interpretation based on facts that happened, it is true, and it follows a logical argument.