In the old pyramid command model, meme fidelity is preserved by authoritarian methods. Everyone throughout the system is forced by various methods to obey the top of the pyramid as accurately as possible.
In a network, where each node is potentially linked with every other node, or has to rely on bridge nodes to relay the meme to new networks, meme fidelity has to rely less on authoritarian methods, and more on how much each node likes the meme. If they don't like it, then the meme transmission is immediately stopped (although other nodes may still transmit the meme around the blockage). If a node doesn't think the meme is perfect, then the node may rewrite it in a way that they think is better. If some parts of the meme are liked so much by some given node, that node may obsess over it, and transmit that part of the meme even more earnestly than the source.
Each node in the network applies their own filter to the memes passing by. Unpopular (or incomprehensible) memes are quickly contained and filtered out. Popular ones spread like wildfire, spawning all sorts of variations and improvements, even applications in unintended branches of knowledge. Attempting to maintain fidelity is a losing battle though. Eventually the meme will have to cross the language barrier, where fidelity is very difficult to maintain. Even if you manage to preserve a language across centuries, the changing context around which the language operates, will result in different interpretations of the original message.