Are there genetic factors that biase the sex ratio of offsprings for each person but average to 1:1 for the entire human population, or does the 1:1 ratio apply to every single fertile person?
The ratio you are referring to is indeed computed aggregating multiple observations and thus it is a "statistical average".
Any individual (or couple, in this case) can have a specific ratio that differs from the average one. Many factors may affect sex ratio, among which sperm/egg viability, chromosomal aberrations, and hormones misbalance are the ones usually affecting the fertility of a couple and they can also bias the sex ratio.
Many other factors can play a role. Different populations have slightly different sex-ratio and even smoking can skew the sex ratio!