So an unnamed senior official!!
Knowing Indian media pretty well, I could say with certainity that they cooked up this remark.
While it is true that S-400 at border would be able to shoot down any aircraft in Pakistan air space theoretically, in practice doing so has certain problems.
1. S-400 would not be stationed next to border ,least it be targeted by artillery/MRLS fire. It would be stationed a good fifty to hundred kilometer or so inside the border which means that its range would be reduced by that much.
2. S-400's (40N6E) longest range missile is bulky and unsuitable for targeting nimble fighter jets. It was designed to take down AWACS and EW planes of USA, and at its extreme distance, it would only be able to intercept PAF's air-refuelrs and AWACS.
3. The 400 Km range of 40N6E is in head chase mode. In normal scenario, this range would be less than half of this.