After testing the vba code, I confirmed that there is an issue in the IntersectWith statement in Area 2. I don't know how and why this is happening but IntersectWith detects 2 intersections in Area 2. We can discard the other intersection (via Redim - see code) if you will use the code on polylines with only one real intersection, hoping/assuming that vba finds the real intersection first. 
here's the modified code.
Code:
Sub IPNT()
Dim Poly1 As AcadLWPolyline
Dim Poly2 As AcadLWPolyline
Dim pts As Variant
On Error Resume Next
ThisDrawing.Utility.GetEntity Poly1, pickPt, "Pick Poly1:"
If Err Then Exit Sub
ThisDrawing.Utility.GetEntity Poly2, pickPt, "Pick Poly2:"
If Err Then Exit Sub
pts = Poly1.IntersectWith(Poly2, acExtendNone)
MsgBox "Found " & (UBound(pts) + 1) / 3 & " intersection/s."
'-----------------------------------use this to use only the first intersection
ReDim Preserve pts(2)
ThisDrawing.ModelSpace.AddPoint pts
'-----------------------------------use this to use only the first intersection
'-----------------------------------------use this to display all intersections
'Dim ptCoord(0 To 2) As Double
'For i = 0 To UBound(pts) Step 3
'ptCoord(0) = pts(i): ptCoord(1) = pts(i + 1): ptCoord(2) = pts(i + 2)
'Debug.Print ptCoord(0); ptCoord(1); ptCoord(2)
'ThisDrawing.ModelSpace.AddPoint ptCoord
'Next
'-----------------------------------------use this to display all intersections
End Sub
...and please use [code] tags for easy code reading. Good luck.