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.
Did you turn your phone's timer ahead for some reason? Chances are that is the cause of your issue if you did. If that is indeed the case, I am not certain of this but, after the amount of time you jumped passes your explorer should start encountering creatures and collecting loot again.
Best Answer
Based on what I've read scrounging around the internet, it appears that the answer is no, Bottle and Cappy do not affect wasteland events.
From Section 20.9 (How do random quests with explorers work?) of therabidsquirel's The Fallout Shelter FAQ:
From Section 21.2 (What do they do when they visit?) of the same wiki, what Bottle and Cappy do affect is as follows:
The Fandom pages for Bottle and Cappy support the latter and neither make any mention of having any affect on wasteland events.
According to this Gamespot article, Bethesda released this statement regarding the Fallout Shelter 1.7 update:
From Bethesda's statement, it would appear that Bottle and Cappy were only ever intended to produce a few extra caps and Nuka-Cola Quantum for the player.
This Eurogamer article for the same update says more or less the same, as does this Bethesda Support response and this review's screenshot caption.