I have no doubt that the word "Savior" was used here with a different purpose in mind, a more appropriate term could have been used. There is no doubt that India had her own interests in the whole episode, however, there is also an effort here to belittle India's role in 1971. Let's assume for once that Kashmir didn't happen between India & Pakistan, there were no 1948 & 1965, the relationship between India & West Pakistan was favorable, and India decided not to get involved in the 1971 fiasco. Let's go back to 1971 and see how things look without India into that equation.
1. Mukti Bahini: India helped in creating the Mukti Bahini, India provided finance, arms, intel, strategy, training, land to launch attack, land to fall back and regroup, safe shelters for East Pakistani leaders, almost everything that they needed to fight the war. How effective the Mukti Bahini would be without India into the equation? Remember, they had only one friend back then, without it Mukti Bahini would be a ill-financed, ill-equiped, ill-trained force fighting blind without any intel. East Pakistan being a small & flat country, there would be little "safe" place to set up command & control, launch attack & fall back, regroup, formulate strategy and fight as a single unit against a professional army. Add to that, without a safe land to take shelter, East Pakistan would have lost its important leaders to Pakistani army at a high rate.
At worst, there may not be any Mukti Bahini at all, it might be scattered groups of brave souls taking on the Pakistani army without any coordination. No doubt Bangladesh's freedom movement would be in a seriously disadvantageous position without India's help.
2. Pakistan: One thing we can safely say about Pakistani army is that, they are of very persisting nature, they can't really let go things even if the chances of winning it is very slim. They would not let go East Pakistan easily if they were not so decisively defeated by India. And most of the BD members would agree that Pakistan lost there ability to continue fighting in east Pakistan because their supply was broken, by India of course. Now, imagine a completely unchallenged Pakistan with a smooth unbroken supply line to East Pakistan, and things change completely!! They could simply bring another one lakh soldier if required, they could secure airstrips and bring their mighty airforce (Which was really high-tech back then), and crush any opposing voice in East Pakistan. Nothing, absolutely nothing could have stopped them. Well, only conscience could have stopped them, but they didn't show that they had any.
3. With a severely crippled freedom movement (as explained in point no. 1) and an unchallenged Pakistani military, things are already looking hopeless for East Pakistan. Now you can also factor in America & China into the equation. They couldn't interfere as Russia was on India's side, protection from Russia wouldn't be there if India was not involved. Now I will not imagine an American fleet at Bay of Bengal actively participating in the war, that would be too much for East Pakistan, neither Pakistan would actually need that when they are unchallenged by anybody. But diplomatic help and help with support and supply by these two countries would add further problem to East Pakistan. Again remember, even with India's full help to Mukti Bahini, the war could finally end after a full-scale war between to professional armies, and they surrendered to India, not Mukti Bahini.
We should not also forget the immense diplomatic help India provided to East Pakistan before the war, as well as after the war to get East Pakistan recognized as Bangladesh, sadly, still some BD members here never fail to dish out one or two conspiracy theory threads every month to prove that India wanted (or still wants) to annex Bangladesh.
We should also remember the humanitarian help India provided to East Pakistan / Bangladesh by sheltering millions of refugees as our people (And we are still doing that!).
Finally, I wonder whether the leaders of East Pakistan would have taken such a bold step against West Pakistan without assurance of help from India.