If the signal wires / traces for INT0 and INT1 run any distance together (more than a few inches) then cross talk might be the reason. You'd need much stiffer pull ups to prevent that (330 ohm??) or more simply add some 100pF caps to ground at each input to slow the edges down and smear out the crosstalk spikes.
I'd have thought that if you are interfacing two push buttons you'd need software debouncing anyway which will DTRT and you won't need to worry about this happening as it will be treated as a bounce?