A 10k resistor is a 10k resistor in this sense. Even if you had a 10% tolerance resistor you're looking at 9k-11k resistance which is going to amount to a max 0.066mA current draw difference. That's not going to cause a power problem.
I plugged an el cheapo no name 5V 1A power supply in instead of the bench power supply and it works fine on the B+ with ethernet and wifi (which is the most power it can draw). You're not seeing a power supply problem, you're seeing a problem whose effects are happening at the power supply because you can't see what is causing the actual problem. Are you touching the device at all while doing these tests? Bear in mind that the braid of the probe carries current and is connected to ground so if it touches anything, even another something on the desk that is plugged in, you're creating a short.
The probe type doesn't matter either, if you're saying to reboots with just the 10k resistor, there's no probe involved, right?