I've heard, anecdotally, that part of the reason behind Japan failing to follow up the Pearl Harbor attack with a strike on the US mainland was a fear of American's widespread ownership of firearms. Is there any truth to that statement, even in the slightest?

Absolutely 0 truth to it in any convincing way and on multiple fronts.

The first being that quote often used is fabricated wholesale and often attributed to Yamamoto. And while he did remark about in order to truly extract victory and concessions from the US that terms would need to have been dictated in the White House it was exasperation of a different sort. He saw no willingness by the US to cut it's losses after initial defeats and before the grinding calculous of population and resources took over. While also speaking to the difficulty that a small island nation would have in striking a knockout blow across 5000 miles of sea and another 2000 of enemy territory.

On the second front it was simply beyond the capabilities of the Japanese war machine to follow up on their opening gambits more than the did really. Virtually every warship and the majority of their auxiliaries and merchant shipping was accounted for in supporting the Pearl Harbor strike, and the drive on the Southern Resource Area. And while perhaps more army units might have been drawn out if China they were useless without ships to carry them. And every force diverted from the drive South took away from the entire reason for war as it occurred in late 1941. That of securing the resources needed to fuel the war economy to support the fight in China. The Pearl Operation was very much run on a shoestring, there were even suggestions to abandon a carrier or escorting destroyers as they ran out of fuel! To say nothing if supplying any landing forces in the Hawaiian islands let alone US mainland.

So even just landing a credible force in Hawaii was simply not realistic, and had it been it would have badly distracted from more important goals.

All this completely separate from how many if the locals were armed.

For more on the logistics of the IJN I would point you at "Shattered Sword" by Parshall and Tully. They also run the excellent CombinedFleet.com which has more pieces looking at the feasibility of landings in Hawaii. There are plenty if other works but the duo is very readable and a fine introduction.

While as an aside the IJN DID strike the US mainland as best they could. Prepositioned I-Boat subs were situated between California and Hawaii when war came with more surged in support for a few months into 1942. They sank a gaggle of ships, shelled a handful of coastal sites and caused a bit if panic before fuel and food limitations inevitably forced their return home.