Dear Challenged by Passport:
First of all, Congratulations! Now take a deep breath - you are fine!
The information from some websites that you have quoted is wrong. The passport should be valid for at least 6 months at the time of entry into the US, NOT at the time of departure from the US after completing your education.
You are quite correct in noting that you can get your passport renewed in the US. While the Indian High Commission is in Washington, DC, there are several Indian Consulates scattered around the country, each being responsible for its designated region. You can get your passport renewed, from your regional Indian Consulate, within the 6-month period prior to its expiration. This process can be handled through the post. You need to submit your passport, an application and required documentation, and a renewal fee. The entire process takes 2-4 weeks.
So put aside your worries and get started on your new exciting adventure.