I agree with this as a general statement, but you risk oversimplifying things. In general, I have seen countless instances of people who have taken "a degree" (regardless of what it was in and where it was from) and worked hard in their chosen field and advanced on their merit. For example, a friend of mine who is a successful pharmaceutical sales rep graduated from Allegheny College with a degree in Communications.
I also agree with this, in that, most of the people who think that they should/will get a job based solely on the degree they earn will end up being bitter and disappointed in the result. I don't care who you are or where you are went to school, this all goes out the door when you start working. As such, if you are earning a degree, you should spend a significant amount of your time on career and professional development. The students who do internships (particularly those who do several in many different organizations and jobs) are far better prepared than those who simply go to school and hope for a job one day.
This said - the student who makes a smart decision about what they major in and the career/professional development they pursue in school can absolutely tear up in the job market. For example, I went to Purdue for undergrad. My roommate graduated with a degree in Mechanical Engineering, which is no small task. He had 4 or 5 internships and research projects while he was there, and has had an amazing career in which he has worked in several great jobs, gone to graduate school on a full ride, and lived all over the world.
A more recent example is my ex-gf. She graduated from Pitt with a degree in Accounting. She did internships in accounting firms, a local healthcare company and was a teaching assistant. Recruiters were clamoring for her from consulting firms, because they knew she had the knowledge and skillset to go to clients. She constantly looks at the job opportunities available and moved from consulting to internal audit two years ago. She has since been promoted three times in her new company (a large national bank) - largely because her bosses know that she can leave for other companies.
Bottom line - the degree is great, but what you do with it is up to your hard work and the opportunities you make for yourself.