Alaska has no law requiring firearms dealers to initiate background checks prior to transferring a firearm.
Neither does New York. Federal law applies, as in Alaska.
As a result, in Alaska, firearms dealers must initiate the background check required by federal law by contacting the FBI directly.
Right. Just as in New York and 30 other states.
Federal law does not require dealers to conduct a background check if a firearm purchaser presents a state permit to purchase or possess firearms that meets certain conditions.
Right again. New York's CCW used to provide exemption from NICS. That privilege was yanked when the Feds decided that New York's record-keeping was too sloppy. Alaska allows concealed carry without a permit, but one can optionally get a permit if one wants to be exempt from NICS. The Feds still recognize Alaska's permit as a valid NICS exemption, which would suggest that Alaska's procedures are aboveboard.
As a result, holders of concealed weapons permits marked NICS-Exempt in Alaska are exempt from the federal background check requirement.
Right once more. The permit holder has been sufficiently background checked to satisfy the Feds, and is therefore able to benefit from the NICS exemption.
To summarize, Alaskans can carry concealed without a permit, but must undergo a Federal NICS check in order to purchase a firearm. If they wish to be exempt from NICS, they must obtain a permit. Alaskan CCW permit procedures are more stringent than those in New York, as demonstrated by Federal recognition of the former but not the latter.
Where's the Catch-22?