...Even stranger is that the incoming transfer from another mybitcoin user with which I funded the outgoing transfer is not present in block explorer either! It seems I never had the money I never received. 
...
...This particular detail is consistent with how it is advertised. MyBitcoin-to-MyBitcoin transfers are done on MyBitcoin's records and not on the block chain.
That's good to know, especially when searching block explorer - coins involved in a transfer might come from some other address.