don't understand why it causes it to not work when it's supplying the same amount of power as the usb cable, but maybe 1 amp isn't enough...
Keep in mind that Voltage, Current, and Power are all very specific terms. They are very different (related) things, but you are interchanging their usage. Voltage is "Pressure", Current is "Flow", and Power is a function of both. Power = Voltage times Current
Current is "sourced" and "drawn." So a source rated for 1Amp means it is capable of suppling 1Amp. A 7805 (and similar linear regulator) can source 5V @ 1A if they are properly heat sinked. (Which would be 5V * 1A = 5Watts of Power.) Other wise their output capacity could be as low as 100mA.
So your comment "they provide the same power" isn't correct. USB and the Regulator both provide 5Volts. However, their Power capability is different since USB only sources 500mA and the regulator can (under the right conditions) source 1A.
It sounds like you were connecting your 5V regulated output to VIN and not the 5V node. So the on board regulator was trying to regulate 5V-in to 5V-out, which doesn't work.