You are right, the spot exchange rate at a given point in time is random and tells you nothing (nothing!) about the value or strength of a currency. Japan is a great example.
What, however, does indicate a weakening or economic downturn is the uncontrolled depreciation of a currency, which errodes savings, threatens foreign debt paybacks, and makes imports more expensive
The Yen is relatively stable for decades at its spot. The Rubel is sliding against monetary and fiscal efforts, which indicates deeper macroeconomic issues.
People aren't talking about absolute value. Being worth 0.01 of one dollar or 300 of one dollar doesn't say anything.
People are saying it with the context of the previous value.
If there is a headline saying Euro/dollar has reached 1.30, no one should be responding "so what, the Canadian dollar is 1.35". Because everyone knows the context of Euro/dollar not being near that rate for a long time.