Should I not apply to a PhD program when a Potential Advisor gives me a generic response?
In managing responses, you should keep in mind the policies and procedures of respective departments. For instance, in my field, projects aren't discussed until after a student's been admitted, and the decision regarding advisors isn't made until after students enroll. So there's little productive reason for an advisor to discuss projects with prospective students, given the enormous time between the conversation, and when the student would start working.

In addition, keep in mind that professors are busy professionals, and have lots of demands on their time. For instance, the professor you've written to might be on travel, or have some ongoing commitments that preclude a longer answer.

Now, on the other hand, if you're submitting to an individual PhD position, and the professor will hire you "directly," then a generic response isn't so good, unless there's an indication that the professor would like to discuss things further. 

Finally, how generic a person's response will be will also depend on how generic or specific your initial inquiry is. If someone "cold calls" me, and "greets" me with "Dear Sir" or "Hello," and doesn't show any signs of explaining why I should consider hiring that individual, I am unlikely to respond at all, because why should I write a personal response to a form letter?