an antenna has an impedence at the frequency it is being used at, and an
impedence at its resonant frequency. If either of these impedences happen to be
50 ohms and the coax being used is 50 ohms, and the transciever is working at
50 ohms, then the swr is 1:1, and the swr is on the transmission line, not on
the antenna.

The antenna does not have to have an impedence of 50 ohms at either the
frequency being used at or at its resonant frequency, and these two freqeuncies
could be the same, and the transmission line does not have to be at 50 ohms,
and for that matter neither does the transciever. If any one of these is
mismatched, then the swr is not 1:1.
An impedence transformer at the antenna-transmission line junction will
transform a mismatch so there is no reflection on the transmission line, amd if
this impedence is the same as that of the transmitter, then the swr is 1:1, if
the impedence is not the same, then the swr is not 1:1 unless it is also
transformed at the transmitter, and again the swr would be 1:1 on the
transmission line, which is where the swr is, it is not on the antenna.