Yes if the compressor internally failed, it will fill up/ clog the condenser and must be replaced also (the drier is attached to your condenser so it's 1 piece). The rest of the system needs to be flushed as well.
And probably the expansion valves should be replaced as well, which is really labor intensive as it requires pulling the dash. I think that shop was planning on just flushing to take care of the expanding valves to avoid the labor involved in replacing those.