She is correct.
Some companies only change the packaging on the one year and three year vaccines to meet different state requirements.
It works for at least three years. I can't answer the question about your particular county.
I don't know why some people on YT are nervous about the three year vaccine. Perhaps they think it is three times as potent?
If you do get the one year vaccine when they are adults (even if it is really the three year packaged for one year sale), you may have to vaccinate the next year because one year is all that that label said it was good for. Hard telling with some states and companies.
Defensor I and Defensor III are said to be the same with different packaging.