Hello there!
There is no such case where IIMs are always back of the branding , they are just our assumptions. While many of the local BBA college student’s are making into top IIMs just based on their personality , CAT scores & previous scores . Its not abt the previous college but compared to Engineers , Non-Engineers have more chance’s of getting into top IIMs. So chill up and have a good CAT score and Impress the Interviewer’s during your Interview section.
I have answered a similar question on Quora , please have a look at that . Hope the below one’s will be helpful in clearing the air.