The line positions are 1, 3, 5... and 2, 4, 6... as you stated but they are double spaced in the video waveform, it is the interlacing that sets their positions on the screen, the actual line numbers are consecutive 1, 2, 3.... on one field then 540, 541, 542... on the next field.
When viewed on the screen they are sent as 1,2,3.... but may look like this (example):
1
540
2
541
3
542
A delay during the change from odd to even fields makes the even field appear late so it sits between the lines of the odd field.
Brian.