I had similar weird experiences with my DD, who was about that same age at the time. I was sure she could read, because she acted consistently with having understood something she'd been exposed to only in writing. But faced with a piece of paper, she was unable to read anything - not even "the" or "cat" - despite being desperate to learn to read.
She started kindergarten not reading, and a couple weeks in, something clicked, and she could read almost anything a few weeks after that. She has always been the kid who couldn't do it until out of the blue she could do it perfectly, and reading went that way, too.