The quality of items you find is directly tied to the length of time the dweller is out in the wasteland. Their survivability of course is related to their level (health) and the number of stims/radaways you give them.
Basically just wait longer. The longer they are out there, the better chance of getting a better drop. There are no guarantees of course, but if they can survive out there for several more days, leave them for as long as you can and you should get better drops. Since they take no damage or radiation while on their way back, you can wait until they are literally 1 hp away from death before recalling them to get maximum exploration time.
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.
Best Answer
I would have to agree with @Nelson above -- I think this is just bag RNG luck. I've had several instances where the same level 50 guy goes out and finds tons of stuff, and others where he finds almost nothing. IMO the only recourse is to drastically increase your sample size and send the same guy out lots more times and see what happens. If it's 100% nothing after many attempts, I'd start to think it's a bug, otherwise, blame the RNG.