Okay, after doing some more testing, I can see that quests are definitely used as a base occasionally. However, the chance at a quest being rolled versus a challenge seems to still be much lower. Using the difficult swap trick to refresh explore, I quickly went through 50 more explore screens. Of these, I was able to correlate 43 of them to a specific challenge with one troop swapped.
I’m willing to be the other 7 could bet correlated to quest teams with one troop swapped. Here are the 7 anomalous teams that I saw:
Based on this, I now concur that quests are indeed the mix, but it is heavily weighted against seeing them. Based on the numbers I’ve recorded and hazarding a guess as to how it works based on my personal experience (even this number of battles that cannot be correlated to a specific challenge in the mix seems high to me), it may be that a random quest has about as much chance to be pulled as a base team as any specific challenge, or, basically, 1 out of 8 chance to get any specific challenge and another 1 out of 8 to get a random quest which is then pulled from either all quests or a smaller pool of eligible quests. If not, then the chance of getting a quest team as the base team is purposely weighted against by some other amount.
I know 50 explores isn’t a huge sample size, but were quests 1:1 with challenges as being pulled as explore base teams, 7 out of 50 is one hell of an outlier. Either way, challenges make up the bulk of the base for explore teams.
Side note, for anyone using difficulty change to force the explore to change, you only need to enter the difficulty screen and back out, you don’t need to actually change to another difficulty and you definitely don’t need to change, exit, and change back. This makes it much quicker to get the troops you want (but equally as abhorrent a gameplay mechanic in my eyes, so I hope they never make an event this restrictive again.)