How pedantic do you want to get with this, Clyde?
If you read the rules, technically, there is absolutely nothing that says you're ever supposed to 'randomly' assign an obstacle. At no point in the text, does it give you a clear place to draw obstacles from that aren't explicitly stated in the example.
So, if you're going to 'fudge' the rules to give someone an obstacle for something that doesn't appear under the "Obstacles and Difficulties" section, then it isn't a stretch to make the obstacle the result of someone else's roll, is it?
Full obstacle text cited below.
When you try to overcome an obstacle, you roll dice. Start with one die.
Add a die if you have a trait that can help you. If that trait has any tags
that apply, add another die for each tag. Finally, add any number of dice
from your personal pool of dice (your pool starts with 7 dice).
Roll all the dice you’ve gathered. Each die that shows 4 or higher is a hit.
You need hits equal to the difficulty level (usually 3) to pass the obstacle.
The GM’s jobs: listen and reincorporate, play the NPCs with gusto,
create interesting obstacles, and impose conditions as events
warrant (especially when rolls fail).
Say Yes, Look For The Obstacles
By default, characters can accomplish anything covered by their traits.
They’re competent and effective people, in other words. It’s no fun to
ask for a roll when there’s no cool obstacle in the way. Just say yes to the
action, listen, and ask questions as usual. But also, be on the look out for
the opportunity to create obstacles as the action develops. Because you’re
asking leading questions and listening closely, they’ll be all over the place,
so it won’t be too hard to spot them.
Obstacles can be people (pirates, goblins, imperials, citizens, nobles),
weather, monsters (sky squid, flying eels), situations (fires, falling, being
shot at, chases, escapes) or anything else you can imagine.
If a character tries something not covered by their traits, that’s an
obstacle right there: lack of experience and training. Lots of fun things
can go wrong when you don’t know what you’re doing! Also, players will
sometimes try things they’re bad at so they can fail and add dice to their
pool. It’s a fine move for them and it gives you the chance to create more
trouble, so everyone wins.
I'd also push that the ambiguous "Obstacles... ... or anything else you can imagine." would cover PVP actions, too.