I am an ISSA Certified Fitness Trainer and I have not had a problem with organizations not accepting it. I took my training in 2003 and ISSA is better known now. As far as accreditation goes this link will explain why ISSA chose to take a different route. http://www.issaonline.edu/why-issa/accreditation.cfm
ISSA has also been very good about accepting continuing education credits for college courses and from other associations.