Being a student who has seen the Indian higher education system from the school level to the postgraduate level and been part of lower tier as well as higher tier institutions, I think I can say a few words about this.
When I passed my matriculation and 10+2 level examinations, I did it from arguably a major school in Kolkata affiliated to the CISCE. Cheating was something which was near absent (ofcourse you could still find people who purportedly managed to share the correct option to MCQ 1(a) but it would probably be childish lies).
I went to a lower tier institution in my undergrads and I did see some amount of cheating there, but it was rarely an issue. I saw some in the initial years and it decreased at an exponential level in later years - college authorities began to penalize the students enormously if they were caught, which is how it should be. It had been reduced to negligible amounts by the time I was leaving.
At the top tier institution that I attended for my postgraduate degree, there was no cheating. The reason was simple, you couldn't cheat to pass nor did the students really want to.
Now I think the statement that any exam of this scale in the country has similar complaints is an unfair generalization or plain sensationalization. I don't think so.
I think it depends more on the student demographics. The school level exams that I gave had dead silence in the halls, similar to what I experienced during my postgraduate years. The crop of students matter to a huge extent I think, so does the leniency the institution shows. Both of the above would have merely cancelled the candidate's paper if they were found to be cheating, the undergraduate one as you might imagine would not be so strict, although they did reform tremendously later.
If I generalize now, I would tell you this - A strong application I think can be assumed to be fairly authentic in the sense that although cheating is a plague in this country, one cannot ace an examination by cheating through it, it is merely not possible - sure one can pass an examination but I think that is the extent of it.
Also, I don't think it is unfair to say that a hypothetical candidate who aced exams by cheating at an undergraduate level, would not be looking to get into further higher studies - I mean why would they? They already are acutely aware of their incompetence at some level or the other. Also, I strongly believe that the fact that such a candidate is not authentic will be clear from other sections of their application - they cannot escape without having any reflection anywhere in their application. TOEFL/IELTS/GRE scores, research statement, letters of recommendations, research experience - there will be something off, enough to flag a candidate.
And finally let me put all of my experiences in context by mentioning my reaction to the example you used - the matriculation exam in Bihar. I saw those same pictures on television and to say that I was appalled was an understatement - I had never seen anything like that before. To see the education system being prostituted to that extent made me furious and I am certain nearly everyone I know shared that view. Now, I again reiterate my point, these people will NEVER send an application anywhere.
So, yes I think you can consider most applications you receive to be authentic. If they are not they will be reflected somewhere or the other, enough for you to flag it - email communications, scores etc.
PS: Yes corruption is rampant in India but I don't think it is related directly to the example above. The authorities in the picture above are not exactly on the take I think - they are likely non-existent, or lazy, or just plain scared to do anything to the mob.