Section Access by row will impact all other tables that are joined to the field you are filtering under. It leverages the associative model of qlikview and you have to think how NOT to associate data in order to get what you want.
What you can do is duplicate the table in your data model and qualify all the data fields in the duplicated table so that it does not join to the rest of the data model. The table with qualified field names would not link to the rest of the model and is termed a 'data island' . You can impose SA on the field in the data island and the values in that 1 table would be filtered as you wish. Use fields from the data model where you want secured content and use fields from the regular 'unsecured data model' for the rest of the UI.
You need to be careful in your UI design to prevent inadvertent access to secure information either through user employing many dimension filters to 'triangulate' the results they aren't able to see for example.
This approach may not work with Document CALs which in the fine print require a 'single logical model in the QVW.
But otherwise it can work. You can also pass filters between the data island and the regular model. ...
You could try setting finance table as a loose table, so associations will not propagate through it, only "into" it. Normally loose tables are not worth it (most devs might only encouter them as automatic workaround to loops in datamodel, and as a result, something to avoid as a plague), because you lose all QlikView associative logic as well when there is a loose table somewhere in the path between two fields, but in your model it seems most dimensions are associated anyway through the link table, so the effect might be minimized. You would still lose association when selecting directly in one of the fields in Finance table, so keep this in mind.
That way, Section Access should make selections in Finance table (and reduce accordingly), but those selections will not propagate to the rest of the model. This is a theory, because I have not actually tested it, but in principle I don't see why it shouldn't work.