I am sorry you got that poor advice. I really think acknowledging that the sites has something you want, but don't have/didn't get in grad school can be key. Especially at some sites. Again, not all. But really, I'm surprised by that advice you were given, as any reasonably faculty member adviser or supervsior knows that you are lacking in many things at this stage and...THATS OK. If you weren't, you wouldn't be required to do a fulltime internship to get your degree. Humility and being honest with yourself is always a glowing quality as well.
Now, dont take this too far. Yes, of course there is an element of fit that is about "is this site's offerings, as a whole, consistent with my trajectory and career goals." This does require that you have some kind of demonstrated interest or experience in some element of the work though. This can be very, very broadly defined however. It doesn't mean that you have to want to be a VA psychologist or specialize in PTSD to apply for VA internships. And yes, you need to have basics. If you have never done PE or Seeking Safety..thats cool with us. If you have never done CBT for depression, thats a problem. 😉 If you have never been in VA, that's cool with us. If you have never been outside your university's training clinic, that's not cool with us.