Are these "real" rules for award travel?

F-award travel question:

1:
SFO-LHR-<1 week stopover>-FRA
FRA-SFO with same-day turnround (ie, spend 0 nights at destination)

Is this legal or illegal routing?

2:
SFO-LHR-<6 day stopover>-FRA
1 night stay.
FRA-LHR-<overnight layover, <24 hours>-SFO

Is this legal or illegal routing?


In both cases, a very belligerent CS agent denied both, first because I have to spend "a day" at the destination, the second because I am unable to overnight at LHR when flying from FRA.

What do the flyertalk juries say?