Sparkly, do you know what accredited means? We don’t get to decide who is qualified and who isn’t. There is an official board which accredits colleges, and yes, these places meet all their qualifications.
Sarah Schenirer students get their degrees from Mercy College. TTI from the University of Texas and others.
They are just as accredited as Harvard, Yale, Stanford, etc. They are not as prestigious, but they are accredited.
I know a few people with Thomas Edison degrees (gotten through Maalot, with 30 credits from seminary and 90 credits in one year) who have gone to Columbia. They all said they were well prepared and in some ways ahead of many of their classmates.