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Why is each time constant in this transfer function equal to "open circuit" time constant not "short circuit" time constant?

From this lecture notes, the open circuit time constant approximation:

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How to prove the yellow part? The lecture note mentioned Richard Adler at MIT did prove this but I could not able to find his proof and also don't have access to that.

Basically I want to know why when you calculate time constant for a capacitor you should open-circuit all other capacitors not shorting all other capacitors?
I know this is zero value time constant so C = 0 means that you open circuit capacitors but that doesn't really explain the root cause why each time constant in the transfer function is equal to "open circuit" time constant.


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