False, this is what happens here if you apply for a job you are overqualified for. You do not get hired if there are more suitable applicants. The reason for this is the higher your degree the higher your entry level wage. If a Bachelor is qualified a Master holding degree will not be hired. The most educated person is not always the right person for the job, since as a company you want to keep those people put someone in a position they overqualify for and they won't stick around.
If you need a college degree in the US to get about any decent job the problem is not access to colleges the problem is that your high school system, your mandatory education simply put is bad. Overhaul the highschool system and raise the quality there and you won't have everyone needing to go to college to make a decent wage.
The whole rarity argument is nonsense, since countries like the whole of europe have as good as free colleges or heavily subsidized and still not everyone goes to college and make more than an enough decent living. But they were prepared in High school and we have trade schools for those ages.