Yes I think the claim is true as
If Edge weights are not distinct then we can have multiple Spanning trees
Suppose Consider an example
here we choose edges with weight 1 then with 2 then with 3
In case of 3 if we consider both edges whose weight is 3 the a cycle is formed so we consider only 1 edge by this we can have 2 Spanning trees with same weights
Spanning tree 1 :
Spanning Tree 2:
Let me know if I'm wrong
It depends on whether edge weight is distinct or not.
Case 1: Edge weight is distinct.
MST is unique so Kruskal's algorithm (as its always works correctly to find MST) cannot give multiple MST.
Case 2: Edge weight not distinct
Multiple MST of same weight are possible. In this case Kruskal's algorithm may return different MST.