Is what these brethren do—not fasting Ramadan or breaking the fast إلا بالرؤية البصرية (unless by visual sighting), and delaying the Eid prayers and the sacrifice—based on their understanding of the hadith: "Fast when you see it and break your fast when you see it," while not acknowledging sighting through instruments, correct?

Muslims must fast, break their fast, and pray the Eid prayers with the people of their country, based on the Prophet's (PBUH) saying: "Fast when you see it [the crescent moon] and break your fast when you see it; if it is obscured from you, then complete the number [of days]." And based on his (PBUH) saying: "The fast is on the day you fast, and the breaking of the fast is on the day you break your fast, and the sacrifice is on the day you sacrifice."