That’s generally the case for people who have been in the workforce for a while. But for that 1st job, there’s an advantage to be had in attending a school where the recruiters come to you. That means schools:
- with long-term relationships with a company, or
 - that have a stong reputation for a particular major, or
 - that are geograpically near companies, or
 - have huge pools of students (e.g. big State U)
 
Notice that I didn’t mention prestige of the school. What matters to employers is: what can you do for me?