According to what I was told my a Doc, Yes you could have had the vaccination and not have a scar. I was given one and then a second because the 1st didn't leave a scar. It's also on my early 60's shot record I have.
Mine is barely visible now.
I've was told later in life that if you didn't have a scar after receiving it that you had some natural immunity to it.
Explaination could have been BS too.
Same with one of my brothers and with me too... no scars ever appeared though they did on my other siblings. The military got him again much later and still no scar.