But I want to assume that in case Hitachi EX120-3 requires a viscosity of 22 Cst at 100 degrees Celcius but SAE engine oil only reaches 18 Cst at 100 degrees Celcius, we can't use it.
Generally in my experience Hitachi Maintenance Manuals specify recommended oils by brand (Shell, Mobil, etc) and by the name of the oil. So for instance you would find "Mobilube HD90" or "Shell Spirax MB90". They do not state that a customer can use any brand of oil provided it meets specification "X" in any compartment.
Here is the background on how we ended up using SAE50 TO-4 in our large Hitachi excavators.
The Hitachi recommended oils as per the manual were EP90 gear oils of various brands.
Apart from the Htiachi shovels we had an exclusively Cat fleet using TO-4 products in axles and final drives and we didn't have an extra tank on the lube truck for EP90.
We approached Hitachi for approval to use TO-4.
Their response "We can't approve it. We haven't tested it".
Our reply "We'll happily test it for you and share our results."
Silence from Hitachi so we went ahead and did it anyway.
On the bigger machines with 4 swing drives for our test we switched two to TO-4 and kept the other two on EP oil. At the same time we put TO-4 in one side final drive, leaving the other on EP90.
The oil analysis results were a spectacular improvement in parameters such as oxidation. The TO-4 oil was in far better condition that the EP oil when it was drained for an oil change. It did not take us long to switch all the compartments formerly using EP oil to TO-4.
On larger Hitachi machines the implement pump drive gearbox is a separate compartment to the engine. The recommendation was to use a monograde SAE40 oil. We discovered that most people were using SAE15W40 engine oil in that compartment. To us it did not make sense to use an engine oil in what was effectively a power transmission gearbox. After our test on swing drives we started asking "what if.?" and so we tried the pump drives on SAE50 TO-4. Again the results as far as oil analysis were a spectacular improvement.