Your professor is correct.
Most employers do not give much credence to degrees from "online universities" like University of Phoenix / Axia, AIU, Capella, Penn Foster, etc.
And any university that would award an MBA with only one year of study is obviously disreputable.
However, many longstanding, regionally accredited, and completely reputable state universities now offer courses and even degrees online. This is called "distance education."
The links below are the absolute best you will find. They contain more links to many well-respected state university distance education programs.
What distinguishes these sorts of programs is that the courses are generally transferable between regionally accredited institutions. Sometimes, the degrees offered are identical to those earned on campus.
I would advise you to start by looking at various state universities and check to see if they offer the programs and courses in which you are interested. (Pennsylvania has a great system, for instance.)
Just avoid the "online universities." These for-profit businesses are not the same as non-profits institutions of higher education, and they are notorious for not delivering on their promises. I can also assure you that these degrees are laughed at in academia.
Note: In institutions of higher education, regional accreditation is better than national accreditation. This sounds odd, but I assure you that it is the case. The regional accreditors are:
Middle States Association of Colleges and Schools (MSACS)
New England Association of Schools and Colleges (NEASC)
North Central Association of Colleges and Schools (NCACS)
Northwest Commission on Colleges and Universities (NCCU)
Western Association of Schools and Colleges (WASC)
Southern Association of Colleges and Schools (SACS)
If a program is not accredited by one of these associations, it is best to stay away.
Best wishes to you, and good for you for asking the question before wasting your money!