That too… it is easier to argue for the work visa that a graduate degree holder has some sort of exceptional talent or unusual skill, compared to a bachelor’s degree holder. Also, why would a company that is not an outsourcing company* want to deal with work visas for new bachelor’s degree hires when there are plenty of US citizen and permanent resident new bachelor’s degree graduates?
*Unfortunately, it does seem that outsourcing companies are hogging most of the H-1B visas: http://www.myvisajobs.com/Reports/2014-H1B-Visa-Sponsor.aspx . Note the difference in pay between the outsourcing companies and the companies that are hiring employees to do their own work. The pay levels at the latter indicate that it is unlikely that many new bachelor’s degree holders are getting those jobs (as opposed to the lower end outsourcing jobs).