I've found that what can happen in the large corporate world is that you have Developer teams, Production run teams, various IT infrastructure teams, and the Systems Engineers. Networking gets blamed for every outage because well, they are the common thread that all the bits run over. Storage gets stressed out because it is the last thing anyone thinks about until they need it, and the Systems engineers well the Developers want to play all roles unless they don't want to. Production run sometimes lacks the deeper skills of either programming or IT infrastructure.
Enter Unix Engineers. We are expected to have general knowledge of all IT infrastructure, which we do, we program and script extensively, because our automation depends on it, and we have extensive production application run experience do to managing all the different back end services that everyone depends on. mail, dns, ftp, sftp, web server engines, monitoring, etc. Yes a good sys admin must know how to at least read code and ought to be able to code/script in at least one language even if that is Dos Batch. The problem in the end though is as others point out. The more you know the more production run teams may lean on you to solve their problems. "Just ask the Unix team", Not because it is their responsibility, but because they can solve the problem quickly as they have the widest berth of knowledge.
Coding as a Sys Admin is crucial. Just know when to say I can't(or won't), for your sanity.