Having the "master private key" or really the seed for the hierarchical determination is the same as having your private keys.
A master key allows you to derive an unlimited number of private keys. The method for turning the 24 word seed into private keys is known, implemented and published in the form of BIP 32.
More information can be found here: https://en.bitcoin.it/wiki/Deterministic_wallet
The electrum approach is more foolproof but negates all the benefits of using a HD wallet in the first place - let alone the secureity offered by not needing to load your master private key into a computer.