LFS random discovery : time bash builtin and /usr/bin/time

I'm trying to instrument a bit LFS commands. I often wrap `make` into time + tee.
Exit status is often 0 even if make reports errors. Does time report it's exit status ? or the parameter command's one ? .. well it seems that make or the Makefile was design to return 0 even on 'unexpected FAIL' so time says everything is OK. Meanwhile I googled a bit to investigate and stumbled upon that : http://stackoverflow.com/questions/9715570/gnu-time-and-formatting-output

Ahh noobery strikes again.