Also, in terms of timing, in the case you are talking about wouldn't some of the information still be being received by the hardware serial, just not the correct information?
That would be my expectation too but I often see the reason for such a behavior in the scope output although I don't know what to look for before I do it.
Also, do you have the documentation you read for the differences in hardware and software serial?
Yes, you do also: it's the source code, which is part of the IDE (HardwareSerial.cpp and SoftwareSerial.cpp). I use no other documentation because that's what counts in the end, the code that is executed. For the hardware serial interface you might also need the datasheet of the ATmega328p processor.