Q: Does the US give full, unfettered access to the NCIC database to anyone other than Canada?
No. Federal Bureau of Investigation, Privacy Impact Assessment for the National Crime Information Center, November 7, 2022 (PDF download.)
If the recipient of shared information is a foreign government, access is given on a case-by-case basis.
Section 4: Information Sharing
Only Canada has direct access to the NCIC System. Other foreign governments may receive extracted information from the NCIC on a case-by-case basis. The exchange of NCIC information with foreign governments other than Canada is routed through DOJ’s USNCB INTERPOL.
Concerning foreign fugitives,
Foreign Fugitive File
The Foreign Fugitive File contains records from the International Criminal Police Organization (INTERPOL) and the Royal Canadian Mounted Police (RCMP). INTERPOL records within the Foreign Fugitive File contain information on persons wanted in other countries for crimes that would be felonies if committed in the United States. The wanting country must have signed an extradition treaty or convention with the United States, or the subject must be wanted for a violent crime or otherwise must be known to be violent, armed, or dangerous. The RCMP records within the Foreign Fugitive File contain information on persons who are wanted for violations of the Criminal Code of Canada and for whom there is an outstanding Canada-wide warrant. Only the staff of INTERPOL’s United States National Central Bureau (USNCB) and the RCMP can enter records into this File. (Emboldening added.)