If you read the answer carefully, whatever i said still holds.
The complexity is still O(n^3) but bitset uses compile time optimizations. So instead of doing n operations it does some n/64 operations for each bitwise operation like OR, XOR etc. Here value of n was 2000 only. So in that solution total number of operations performed would be (2000 \times 2001)/2 \times (2000/64) \approx 6.25 \times 10^7 that might be a reason. But still time complexity would be O(n^3) only.
And if you read some posts about bitset on codeforces, it is much more faster than expected.