Islamic events are governed by the Hijri calendar, which is lunar-based. This calendar is equally accurate as the Gregorian calendar and the days of the week for a given date can be predicted just as accurately for any year in the future or past.
The moon-sighting practice is defended by invoking a specific hadith, but in my opinion the interpretation of that hadith is too literal (my opinion is of course in accord with and completely determined by the theological teaching of our religious authority).
So, muslims like myself believe that Ramadan begins on the known date of Ramadan 1st, and that fasting begins on Ramadan 1st. We do not believe that the date of Ramadan 1st is flexible, or that fasting should not commence until the moon itself has been sighted. The basic philosophical difference hinges on whether the position of the moon determines Time, or whether time determines the position of the moon. On that score, I rely not on hadith but on the Qur'an:
[31.29] Do you not see that Allah makes the night to enter into the day, and He makes the day to enter into the night, and He has made the sun and the moon subservient (to you); each pursues its course till an appointed time; and that Allah is Aware of what you do?
[13.2] Allah is He Who raised the heavens without any pillars that you see, and He is firm in power and He made the sun and the moon subservient (to you); each one pursues its course to an appointed time; He regulates the affair, making clear the signs that you may be certain of meeting your Lord.
The moon is servant, not master - and the appointed time governs what I do.