The "muon rider" would find the earth's atmosphere to be very thin and approaching fast, so no trouble passing by within a microsecond. They would find ground clocks slow after factoring light travel time from Doppler blue shift. They would also disagree with earth observers about where the earth was 'at the moment the muon was born'. This simultaneity discrepancy would be large.I have been trying to think of how the reciprocal effect could be 'observed' by the muons. I guess they would see the ticking of the scientists' measurement clocks going very slowly, giving the muon the impression that it is due to blow up much sooner than it expected to, according to those clock ticks.
None of this stuff is intuitive.