I can't believe how much people are obfuscating the obvious. The cop wasn't saying you need to get off and walk the bike to cross. He was just saying that the walk sign applies to people who are walking. If you want that sign to apply to you, you need to get off the bike. Otherwise, you have to wait out the red light because you are operating a bicycle on a way.
Are people really confused by the idea that if they're riding on a road, they're expected to obey traffic signals? OP, you ran a red light in front of a cop and he let you off with a warning that won't even go on your driving record. That's it, end of story.