It is true.
A plane requires a minimum of 3 points. It is always a truth. Any 3 points detrmine a unique plane.
Given a point (say its cooerdinates say 2 dimension or 3 dimensio or higher ), it is unique.
Given two points (the coordinates or location of 2 points) , they determine a unique straight line.
And like that given 3 points in silid geometry, they detrmine a unique plane.
So the 3 vertices of a triangle are always in a plane. Or Any 3 points in space are aways form a plane or they are coplanar.
Any four points need not be coplanar.
Yes, the statement is true. However, it is somewhat confusing. Perhaps it will be better to state that "any three points forming a triangle define a unique plane. That is, all of such three points lie in one and only one plane. All the three points cannot lie in two or more different planes.
Any three points that do not lie on the same straight line, form a triangle. Such three points that form a triangle define a unique plane. Any one or two of the three of the two points can lie on an infinite number of planes, but there is only one plane that can include all the three points.