1) The fact that the very first rep was harder for the rest group compared to the jogging group suggests that the jogging recoverers were mentally holding themselves back in anticipation of the overall effort they could reasonably sustain.
2) The fact that lactate was higher in the rest group is consistent with previous findings that suggest that mild activity clears lactate faster than rest + the rest group was producing more lactate to begin with by running harder.
3) My guess is that walking recovery would be in between complete rest and jogging, not equivalent to complete rest as the article seems to suggest (though the study appears to have not explicitly considered walking).
My personal experience is consistent with these findings: I find myself running my 800 reps 10-20 seconds/mile faster with walk recovery compared to even really slow 13’+ jog recoveries. I run both by feel, so my perceived effort during the reps is about the same (modulo feel accuracy) but I know now not to think my fitness dropped on jogging recovery workout days but rather to expect to be somewhat slower on those days.
My watch seems to give me more credit on walk recovery days, but I think that’s just because it is probably programmed to consider total time spent at faster paces to compute training effect.