The strength of the joint has nothing to do with the issue it is the degree of freedom that limits the ability of the towers to share load.
The side loads you refer to are the loads needed to make the joint fail and they are irrelevant to the argument.
When you apply a compressive load to a long thin strut it will simply buckle (as defined by Euler) and this will allow movement.
If you hinge the ends the column (which is the degree of freedom provided by the heim joint) it will be much less stable than with the ends pinned.
By pinning the ends you effectively halve the effective length of the column and make it much stiffer and capable of transferring more load between the two strut towers.
The compressive loads occur when the car drives over bumps and both wheels load differently.
The presence of the heim joint will allow movement and the compressive load that causes the strut to buckle will allow movement.
If you draw the free body diagrams it becomes obvious.
During cornering on a flat road the bar sees tension and this means that the bar is more stable and the presence of the heim joint has no impact on load transfer.
Pinning the ends of a strut makes it more effective in compression which is the point I was making.