Try and avoid thinking in terms of "at fault". The primary goal is to get the work done. Mostly it never descends into blame storming and fingerpointing - so try and avoid behaving like it's got there before it does.
You don't need to "keep repeatedly asking", but you do need to ensure you've communicated clearly. If you asked for clarification and didn't get a response, follow up at least once, and make sure you follow up when you decide you need to shelve the task until you get a response (possibly in that first follow up).
"Hey $boss, I haven't heard back about the question I asked about $task on $date. I can't move forward without a response, so I'll put this task aside until that's resolved. If it's still urgent or critical, let me know, and let me know if I should continue chasing up that question with you or with someone else. Thanks, $communicative-co-worker."
Your last sentence is key - communicate. Both ways. With the prime intention of getting things done, and clear language explaining when things are stalled at your end and what needs to happen to un-stall them. If you're doing all that - you'll make your co workers and bosses very happy, and you'll have all the paperwork you need if things _do_ end up in a blame storming session later on. But don't optimise for the blamestorming, optimise for getting things done and clear communication...
I'm slightly baffled by the premise of the original piece. If you set a task and hear nothing except "go away and leave me to it" updates for a long time, instead of checking up on magic keys, isn't it more useful to have a detailed progress session? Maybe ask for an approximate ETA?
In a non-toxic workplace it should be possible to do this in the spirit of fact-finding without raining blame on anyone.
The problem with that is that, weighted by number of job openings (for internship/begining/otherwise-not-already-successful candidates), most[0] workplaces are toxic.
If you can find somewhere to escape to, go for it, but sometimes you can't.
0: The exact proportion one sees will vary, but basically bear in mind that if people aren't quitting in disgust, your own workplace is less likely to be looking for replacement shmucks.
In that context there is no blame, there's just information: Work can't be distributed for reasons, reasons that should maybe worry us. One of the least likely reasons is "person X is stupid". Far more common is "person Y and Z have a serious case of the Curse of Knowledge".
YET, if said person raises concerns immediately, there's also the potential for that work to get reassigned in a manner that never gives the said person to learn how to do X.
I agree that this is a selfish action, and ideally we do not act in such ways when under pressure to perform and work as a team. But I've found that this psychology often explains why teams find themselves with facing a Canary MacGuffin.
Blunt answer: yes. Absolutely.
If you still don't get a response after escalating as far as you feel comfortable - then that's what you need to report to your manager, so they can do their job and make sure you get the information you need.
For example, I've asked several times for clarification and got no response back. Now you're busy, and rightly so, you deliver far more than I do, but I considered those ignored contacts. Maybe you legitimately just missed them.
Do I keep repeatedly asking? That's the right thing to do, but as a human, it's a hard thing to do.
The reality is, there needs to be a communication channel back and forth, there is no hiding the details, but the channel needs to be there, and respond. If either side doesn't fulfill that minimum, there is going to be a lack of information.