And there are plenty of reasons to believe otherwise. For one, extensively reading code is rare among coders. All good poets are very well-read in poetry, but there are many good programmers who rarely read code other than what they intend to modify, or as documentation.
Also, unlike a poem, a unit of code (say, a function) has a very well-defined goal. Coders don't need to develop an elaborate aesthetic sensitivity to judge whether their work passes their goals - unit tests and benchmarks will do just fine.
Nor do coders need to read code in order to learn about clever coding techniques. Partly, this is because code, unlike poetry, contains very few clever things per line. Partly, because there are simply better ways to get such information: books, blogs, articles, HN, proggit, stackoverflow, and so on.
It may well be that reading code is very helpful in becoming a better programmer. But I'd like to see some evidence first.