I agree , devices with low ESR e.g. < 10mΩ ( yours may be <<1mΩ) need a substantial Rseries if using Voltage regulation (possible but not recommended),
Buit if using current source then it may have an equivalent ESR when saturated and string of Vf equals supply voltage avail, otherwise {Requiv} of Isource >> Rs. So adding 100mΩ may be useful to spread the heat from current source to series load resistor. Adding small Rs is also useful for verifying current in test, as you did.
The reverse mode I suggested is like a string of caps when diodes are not conducting as Vdd collapses quickly to zero the device with the smallest capacitance becomes reverse charged in the series, Otherwise if all matched ( which they are not) the capacitance divider network decays with equal forward voltage. Obviously LED is more like leaky RC ladder and most white LEDs are spec'd 1~10µA @ -5V which is non-linear, so equivalent to 500KΩ~5MΩ with few hundred ~ few thousand puff (pF){depending on size} near 0V.
As diode goes negative voltage capacitance drops and that device changes charge or reverse voltage even more.
Verifying this requires 100MΩ probe or modelling it with bigger values to prove my point.
As I said, I have done this on a client who used AC drive on back to back series strings and got failures from over-looking effects of capacitance.. including dielectric of potting material around LED terminations in their case, which if equal, improves, if not degrades results. THis resulted in my recommendation to spec in back to back zeners included on LED chip.. Most Cree chips now have this built in.. I did this 5 yrs ago. Most small LED's eg < 100mW do NOT have built in Zener protection, but some do now because of risk that clients run them in large series strings with pulse or rapid decay of supply. e.g. noise pulse.
Thanks for your comments.
If the device capacitance current is neglible compared to leakage resistance then a series string of LEDS when pulsed, ( voltage controlled leakage) is a moot point as they all share the same current , so the device that starts to leak more shunts its voltage leaving the others to share the voltage, so it is a moot point. But with capacitance, the memory creates a non-linear reverse voltage effect on a large series string on the best part i.e. the part with the least leakage.. This in turn causes more leakage when Vr> 5V say from a pulsed 20V string of 6 LEDs or 100V string of 30 LEDs or so. (depending on device size and rating). in such cases, zener protection is mandatory, as CREE has done.