Results from the wasteland are mostly random. It is highly unlikely (but not impossible, as you have the proof in your game) that a level one dweller with wimpy stats comes across the most powerful weapon in the game in an hour of exploration. Your badass explorer with top stats and elite gear might not see that type of weapon after exploring for a week. This is how the RNG works.
Because of the randomness, there is no formula that guarantees that a dweller with X stats and Y gear explore for Z time period will come back with the best loot. What we do know is that having better SPECIAL, a higher level, and exploring for longer periods of time make it more likely that the dweller finds better gear, more caps, and earns more experience than another dweller with lower stats exploring for a shorter time period finds. You can see this at work by looking at the results after multiple explorations. Jericho may not be bringing back plasma weapons and fat men every time, but he should be reliably finding shotguns, rifles, and the like rather than rusty pistols.
The other factor that you haven't mentioned with Jericho is his level. Results in my game suggest that the level of the explorer may also factor into the quality of loot they find (although part of this is that lower level wanderers just can't survive very long). My lower level explorers tend to find mostly pistols, maybe
tl;dr
Yes it's possible. Congrats on your guided fat man. With repeated expeditions, the results should be more in line of better stats + more time = better loot, but there is no surefire way of getting the absolute best loot every time. Improve your SPECIAL, improve your level, send out for as long as possible, pray to the RNGods, and send more expeditions. Eventually you will get what you are looking for.
The only thing which could explain it (besides a bug) is that you may missing some electricity or water. If you haven't enough electricity your food and water supply will fall down and maybe collapse. This will increase the radiation of your dwellers. In some cases they may die on this.
Otherwise, I would say it could be a bug. I've had a situation which was nearly the same. In my case electricity was too low, which leads to the situation I described above.
Best Answer
From this post, based on the organized list of weapons, it seems that, in general, Heavy weapons will do the most damage, followed by Energy weapons.
It doesn't seem like the weapons are classed by type due to statistics, so much as they are classed based on what they actually are. A Heavy weapon and a Pistol that do the same damage should be equally effective when used by a single Vault dweller.
As to your question about stats across gun types, critical chance is determined by a Vault Dweller's Perception, while raw damage is determined by their Strength. Shot speed is determined by Agility. Therefore, these stats rely on the stats of the Vault Dweller who is equipping it. The type of gun does not determine this. If anything, it would be specific to each gun.