Bitcoins value does indeed affect the price of all altcoins since BTC/AltCoin trading pairs are the most commonly used and is usually the standard go to exchange pair on all cryptocurrency exchanges. So can Altcoin break all the relationship from bitcoin and run as a independent currency.
practically all crypto-currencies have a positive correlation among themselves. This means that kriptonok as a whole reacts to the same factors, the general capitalization of the cryptology fluctuates with respect to some external factors, the crypto-currencies, in general, move synchronously.
That synchronous relationship is hard to break in most markets. Imagine a major cryptocurrency suffers a hack or fails, it casts a shadow on all others.