Under ideal conditions, where there's lots of data, each value in a SIP is valid because it has actually happened, and the frequencies in the SIP are the same as the reality. That is, a well-formed SIP is correct by construction. Since the rest is simple arithmetic, avoiding implementation errors and independent validation are both fairly simple.
MCS, generating random values from a curve that approximates the data, is approximate by construction. Also, the number of MC trials has to be much larger than the number of SIP trials, so that we can be confident that the PRNG hasn't handed us a freak. We can only hope to get close to the fidelity that comes effortlessly in a SIP.