...many Muslims do not believe in celebrating birthdays or death anniversaries because there is no historical evidence that the Prophet Muhammad ever did this.
It is quite common for Muslims in rural areas, and also for elderly Muslims, not to know how old they are. My SIL was born in Pakistan (he is now a U.S. citizen), and he says his own Grandma does not know how old shes is. The hauntingly lovely girl that National Geographic photographed for their cover some time ago, and who is now a young, married teen (they re-interviewed her recently) is a rural Muslim. She also does not know exactly how old she is. Modern, urban Muslims, whose births are much more likely to been registered, do know. You are correct about Muslims and B-days.