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The metaphor should be very accessible for a fluent speaker of Russian, therefore I suspect that the misunderstanding possibly involved some additional words that also occur in the quote.

In Russian, "to solve a problem" is "решить проблему".  ("решить" is the verb.)

With a suitable prefix, we get "отрешить" which means "untie" or "detach".  The prefix "от-" has two semantic effects:
1. it makes the meaning perfective (i.e., "to detach"); however, if you want to keep it imperfective which keeping the prefix, you can use a closely related "отрешать" (i.e., "to be in the process of untying").
2. it [modifies the meaning](https://en.wiktionary.org/wiki/%D0%BE%D1%82-) as if you added "away from" in English.

The relationship between "решить" and "отрешить" is as obvious as one can be.  It is the simplest verb to verb derivation process in Russian and it is still productive across the board.  This should therefore be enough connect a "problem" to a "knot".

However, let me add that the verb "решить" also means "to decide". Furthermore, the etymologically unrelated but semantically perhaps close "[от]резать" means "cut [away]".  Therefore, if a knot represents a problem, solving it could, for a Russian speaker, sometimes entail complicated untying, another time cutting it abruptly like a [Gordian Knot](https://en.wikipedia.org/wiki/Gordian_Knot).  So "решить" doesn't necessarily imply any slowness or complexity, but rather just getting rid of the problem.