Yes, I have evidence that the POI will change, but when you're dealing with fletched arrows, the POI may change in unexpected ways. When shooting a bare shaft (RH) a too stiff shaft will predictably impact to the left of the desired POI, while a too weak shaft will impact to the right (absent deflection off the strike plate). If the same physics held for a fletched shaft, one would expect that increasing stiffness would move the POI further to the left, and vice versa. However, my own experience, Rick Welch's experience, Fred Asbell's experience, and the experience of a local bowyer, indicates that the opposite is often the case: increasing the spine of a fletched arrow will often move the POI to the right.
I first heard of this while shooting in a tournament with the local bowyer many years ago. I was consistently hitting left, and told him I was thinking of trying some weaker arrows. He suggested that I try stiffer arrows first. At first, I thought I had mis-heard him, or that he was not thinking clearly about what was happening. But on further questioning, it became clear that he was saying exactly what he meant: decreasing my point weight moved the POI several inches to the right. I observed Rick Welch do the same thing for a student in a class several years later, with the same result. Fred Asbell says essentially the same thing on p. 78 of his book, Instinctive Shooting. For years I thought that was a typo in his book, but he wrote what he intended to write.
The reason a bare shaft impacts to the right if it is underspined is because it leaves the bow in a nock left position, such that the shaft is pointed to the right of the intended POI. Since the crabwise orientation is not corrected by fletches, the shaft continues to move to the right in flight.
The reason a fletched underspined shaft often impacts to the left of the intended POI is because flexing causes the shaft itself to move sideways to the left on being shot. The flexing also causes the shaft to point to the right of the POI, the same as a bare shaft would. Without fletches to correct the orientation of the shaft, a bare shaft continues in the direction it is pointed and impacts to the right of the POI. If fletches correct the orientation of the shaft too quickly, however, the arrow is still several inches to the left of the desired flight path and will impact to the left of the desired POI. Stiffening the arrow causes it to be deflected less to the left on being shot, and thus can move the POI to the right.
As you can see, the actual POI of the arrow is the result of several interacting factors: the amount of sideways deflection of the shaft, the angle the shaft is pointing, and how quickly the fletches correct the flight path of the arrow. So while shooting a stiffer shaft won't always move the POI of a fletched arrow to the right, it will sometimes, and is a useful thing to know.