You can certainly have a downbeat start at any frame location, provided you are willing to modify tempo and perhaps time signature adjustments (which is typical).
Some things to pay attention to:
Have the correct frame rate of the video set in Logic
Do not use negative bar numbers - start the project at 1.1.1.1
Have a tempo marking at 1.1.1.1
So very basic example (I use markers and I use key commands). Let's say I have a cue start point and need a downbeat x seconds later to match an on-screen event.
I always have some pre-roll - my cue my not start until bar 5 or whatever... so I have a tempo at 1.1.1.1. This tempo is arguably not important, because my cue doesn't start here.I will put a marker here. I will then go to bar 5 and put in a marker. I will then point another marker at the on-screen event spot (you need the key command set marker without rounding and also go forward/backward one frame).
What I will do at this point (actually, I wait until all hit points are marked) is open up the tempo list tab and in the options menu select the tempo operations.
In the ensuing box, select Operation>create constant tempo.
Make sure padlock icons are LOCKED in position and time fields.
Having set up key commands for Go to next/previous marker, I will go first marker, 2nd marker, etc. The values in the position and time fields reflect the left and right marker locations. Assuming you are going to adjust the tempo, edit the right position field to reflect a beat. So, if that field says 10.2.3.178, I could type in 10.1 and then it would be a downbeat (the tempo adjusts accordingly) if that's too much tempo adjustment, I might type in 10.3 and go back and make bar 10 a 2/4 bar. You get the idea.
This works if done correctly. The Tempo Operations window can be quirky, if you think you're doing it right, close it and re-open it. Also SMPTE lock ALL markers before you modify any tempos!
If you just have one hit point to lock to, there is a slightly easier way, but this method works well for me with multiple hit points. You may well get other opinions....
Lastly, remember you can have alternate tempo and marker tracks.
Hope this is clear enough - it's pretty detailed and I'm not a patient typer.....