It has been my experience that every DMM I have ever used is incapable of accurately testing a transistor or diode.
Why?
The voltage and current on the leads is inadequate to overcome the junction voltage to get a real test of leakage.
I can put a known marginally leaky transistor on any of my DMM's and it shows fine. (Even my Flukes).
If I test the same xistor on a VTVM, Huntron Tracker, it's Heathkit clone, curve tracer, and on my B&K 501 curve tracer. it will show the leakage.
You may argue this point, but this has been my own personal experience many times in servicing over the years.
My Huntron Tracker and my Heathkit clone of it have picked out many leaky transistors by looking at the "knee" junction. I have seen the meter change readings on a VTVM, as current flows in the device under test.
i have come to believe this is because most DVM's use limited current to the test leads.
I never had any problem with the older equipment, just when I went to DMM's.
EDIT: If you build and use an 'Octopus" using a 6.3V transformer and resistors from some old articles, be aware that it can destroy dioses, especially Germanium types like the 1N34.