I know that my son can also get a slight blue tinge to lips and even fingers when he is cold. It happens in the swimming pool a fair amount for example. However, here is what I have learned. You know your child and what is normal. You also know what does and doesn't "feel right". Trust that. If you are not comfortable with what your Dr. is saying, it's good you are seeing another. I'm sure all is fine...you actually do hear about this a lot, and I know from experience it is very difficult to get an accurate reading for oxygen saturation on an infant and toddler. Take good care, and I'm sure this will all turn out well.
I can imagine you feel worried blue lips seem to be a common occurrence, and very often there is nothing wrong however good you are going to have it checked out, we have a cardiology pediatric forum on MH take a look you may find other children with the same .Good luck let us know what the cardiologist says ..