Yes, the state government matters. Jadavpur U was slated to be converted into an IIT, but the WB govt did "let go" of the University, hence the idea had to be shelved. If the state does not agree, it does not happen.

Here's the 2005 news report.
https://timesofindia.indiatimes.com/city/kolkata/iit-status-in-sight-for-two-bengal-varsities/articleshow/1088445.cms