It sounds like she has the essential underlying skills to read, if she's made it through the whole PA ladder, and nothing else about her cognitive profile stands out to you...so maybe she's just not at that place yet, in terms of maturity/patience.
Do you feel like she is trying hard, not succeeding, and frustrated, or do you feel like she is having fun with the computer program, and just not ready to invest the time and attention into independent book reading? If, independent of any other person's involvement, she is unhappy with her reading progress, I would consider continuing to problem-solve obstacles to reading development. If she's happy with her reading skill as long as no one asks her to do a reading activity, then I would say keep an eye on it, but don't worry too much for another year or so.
In addition to phonological awareness, reading requires working memory, attention, sequencing, organization--executive functions that may not be all at the requisite level for reading in a perfectly normal four-year-old. Cognition, oral vocabulary, and even motivation may all be there, but if the frontal lobe isn't on board yet, you pretty much just have to be patient. (If you still have concerns in another one or two years, executive functions is where I would start looking.)
