MTV Unplugged is not live hence why everyone who goes on there tends to sound good because they edit vocals. Same with Victoria's Secret. Katy just really sucks live. Including acoustically. The sad part is you know she tries really hard unlike Britney and Rih who half ass a lot.
This is right.
The performances on MTV unplugged are pitch corrected - see Rihanna's performance of take a bow for blatant evidence of this. The performances on Ellen are also edited - see Gaga's poker face performance there. + Katy's Victoria's secret Firework performance was also edited.