As a shop teacher with 30+ years of history around woodworking power tools and 13 years in the classroom, I have seen accidents and results of accidents from chop saws, table saws, lathes, jointers, band saws, sanders, drill presses, and everything else. Fortunately I've not had to deal with students suffering injuries likely to change how their hands work, but I've seen that and worse happen to adults and children elsewhere. Use the right tool for the job, make sure you prep it correctly, and be thoroughly trained. Students should work within sight of a responsible adult and always check to make sure what they are planning to do is correct and safe.
Regarding bandsaws being a "safer" choice: see the meat packing industry and what they use band saws for.
