My understanding is that I would have no current flow in that direction if my meter could not over those two diodes.
Most transistors do not have resistors. It is true a B-E is much like a diode. Most modern meters measure resistance at a very low voltage so silicon will not turn on. (<0.4V) That is why you can clearly see the resistors with out the "diodes" turning on. Most diodes tests are done at a voltage less than 5 volts. A normal diode has not problem with >5 volts. A B-E junction will breakdown at a voltage in the 5 to 10 volt range. (depends on type of transistor) My meters output 2.5volts in diode mode. They do not measure current but voltage. (depends on type of meter) Most of my meters output about 1mA and measure voltage. A diode will read 0.6 to 0.7 (volts) in one direction and 2.000 flashing (or over voltage) in the other direction.
"Some where in a data sheet; you will find the accuracy of the 5k + 150 ohms is not good. (Motorola 8k + 120)"
Some transistors will read 5k and some 8k depending where they are made. (I think +/-30%)
I did a job or a audio amp company. When a amplifier comes in for repair they replace all the big transistors. With out testing them. They had $100,000.00(s) of dollars of transistors in pile and I found 3/4 were good. Because these parts had seen too much current I was careful. Some of the transistors has the first transistor dead (shorted).
This is what I did.
1) Connected a resistor to the base (to input 1mA) and looked for about 1.4V on the B-E. A reading of 0V showed a major silicon meltdown. A reading of 0.6V showed one of the transistors was shorted.
2) A Darlington should have a very large gain. Look at the data sheet. The current gain has a very wide range. (maybe 1000 min and 10,000 max) To test that. I used the 1mA into the base. On the collector I had a 4 ohm resistor to 5V. (When full on the C-E voltage will be around 1V) (can use a 5V light bulb) If the gain is above 1000 the C will pull low and light the light. If the gain is less the 500 the light is off or dim. (if only the big transistor is working the gain will be 40 to 200)
I measured if there is two B-E junctions from B-E and measured gain. (above or below about 1000). This way I have two chances to catch a bad Darlington. In my case I did find Darlingtons with only one transistor working.
In your case where the parts are new, this is probably too much testing.
It is a good thing to test NPN or PNP by looking at the base. Some times some one grabs the wrong box of parts.