Wow, that really diverges from manga.

But the more important question is: does it diverge from the original light novels? Because if the answer to that is "no," the manga adaptation is the one that's diverging.

Warning: this comment contains episode spoilers (continuing the discussion of the episode accuracy). I've only read the LN, not the manga, but nothing that happened from 16:46 onward was part of the LN. They honestly did a good job stretching out that text as much as they did, but I suppose they could have filled the episode by stretching out her hunt and inserting even more war room talk, etc. Only speculating here, but perhaps they decided this side quest would be more interesting for us? Can't say I disagree, except it kinda messed with the relationship between the captain and Mitsuha. Here's how it happened in the LN: "The mercenaries knew they were traveling to another world. Mitsuha’s visits and behavior up until now were strange enough, but the way she had showed up this time left no room for doubt. Most of them had readily accepted the fact, and no one really questioned her about it. Just like Sven and his people, they respect their employer’s privacy. Must be a merc thing." And that was it. No questioning by the captain, no Humvee scene, etc etc, they were just ready to trust her and do the job. Obviously the captain believes her now, so perhaps no harm done. Hopefully it doesn't waste too much time in the next episode.

The manga basically follows the LN as explained by miniika. There is no Humvee scene with the captain in the manga either.