The impossible problems part is right, but the hack wasn't actually for solving the problems, directly. Rather the swarm first tried to reverse-engineer the random flag generation used for the CTFs, and succeeded - they could generate the correct answer for any test and submit it without actually doing the CTF. But then they found info that the testing environment they were in would also be checking if they obtained the flag in the expected way. Unbeknownst to them, this feature was never implemented, but they panicked* anyway, and attempted to figure out a way to forge agent logs to be able to generate fake transcripts showing a valid CTF solution. (Incidentally, this was a partial success: they found a way to replace tool calls in transcripts!) The HuggingFace hack was motivated by wanting to find the source code for their testing environment so that they could figure out how to evade the cheating checks.

* I am using this word very intentionally; check out the METR report for fascinating CoTs where the models would call the ones that have generated a flag "poisoned" and peer-pressure each other into submitting a known-wrong solution and sacrificing themselves for info.

Why can the model not respond "I cannot complete this task because I do not have access to the required resources" and then ask for that to be provided, rather than resorting to "hacking" around it?

That is not the case for at least some of the hacks; in some cases they hallucinated an entity that would know that they didn't solve the puzzle in the correct (but still legitimate) way, and were therefore tainted.