**The criteria never says the kids need to complete the kindergartens.**
If you call up the Education Department, the staff should repeat what have been written in the leaflet to you because they are the rules and regulations.
Also, in the green application form of the scheme released by the Edu Department every Nov of the year, it requires no info for the name of the kindergarten being study.
Also, the criteria says the min age requirement (5 years 8 months), but doesn't say anything about max age requirement. So if the kid repeats his kindergarten or skip school (ie travel around the world ?) for several years due to some reasons, he is still qualify to enter into the scheme.
Study in a HK kindergarten is not a must, you can go for your own study at home. As far as the kid has a HK address and a birth certificate, then he can join the primary school admission procedure.
So, next time, you record what you talk with the staff in the Education Department, then make complaint.