You are lucky to have only known friendly priests then!! The same priest who I know who refused to baptise babies also refused to allow some children to make the scarament of the eucharist too, again because they weren't at mass each week. He was also the designated priest at my upper school and I remember that once, during a school mass, he actually refused to give the host to one of the pupils because, and I more or less quote, said pupil had "omitted to bow his head when saying the name of Jesus during the Hail Mary"!!!! Weirdly I came to know this priest quite well in my mid 20s and found him to be a very lovely man, but a priest who stuck to tradition and stood firmly by what he thought was right; I suppose that is a value we should expect from priests.
I am actually disgusted. My local Catholic priest used to be in my drama group and is always in our local pub having his pint. There definitely isn't such a thing as being refused in my parish!! 
