According to the German law (§ 68 AufenthG), you do not need an "official invitation letter from the Ausländerbehörde" (the law says that you need an 'Verpflichtungserklärung', but it does not say that it should be approved by Ausländerbehörde). You could write 'Verpflichtungserklärung' by yourself, just by hand. I also do not think, that German Consulate in India is right about it, however, they could have some internal country-specific rules.
EDIT: From my experience, German Consulate is not completely right, or you just do not know their reasoning. It makes no sense for them to ask for hotel, since the accomodation will be at your apartments. However, I'm not sure if your should push them, maybe the hotel will be an easier way...
If you will decide to push them, this could be a useful link:
However, probably, you first need to get a "decline" from the consulate to write a complaint on it. So your parents will not get to Germany so fast in this case.
What I would try to do, just call the consulate and talk with them about the situation. Or directly ask for the phone appointment with the embassador. Usually, an embassador is obliged to have some time for conversations with "usual" people.
2 more things to consider:
For the formal Verpflichtungserklärung, there could be also different text in it. Depending on the State of Germany where you live and your financial status, it could be written there, that your financial status is not proven/enough and so on. In this case the people you invite should show that they have enough money for the trip.
Maybe your appartaments are too small (12 square meters per person, http://www.ailebirlesimi.de/html/ehegatten_von_auslaendern_in_deutschland.html?t=)