How strong is a lag bolt through the narrow face of a 2x4 stud (meaning it only has 1.5" to grab)?
An alternative is to use the flat stud in conjunction with one of the new style toggle bolts.

Now you have a 2+ inch piece of metal placed behind the shallow side of the stud. It would take many hundreds of pounds of force to pull that little steel bar through the stud.
You would need to drill a slightly larger hole to accommodate the toggle.
All of this assumes that the flat stud is not backed by another stud. If that were the case, standard lag bolt approach would have plenty to grab and a very rigid structure.

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