Hypothetical: building an free-standing cabinet wall
A lot of the strength of a wall comes from it being anchored at both the top and bottom. If you only have it anchored at the bottom, your concern that the wall would lean or fail entirely is well-founded. Building a false wall is not a terrible idea, it just needs to be built correctly to handle the expected load. You could also attach directly to the (presumably) concrete block walls using appropriate fasteners and methods.

I would double check that you would even need permits and an inspection. Cabinet installation is not something that usually does, even in basements.