Let's examine the game text of two cards
Strength of Spirit:
Spell. Response: If a companion is about to exert, spot Gandalf to place no token for that exertion.
Intimidate:
Spell. Response: If a companion is about to take a wound, spot Gandalf to prevent that wound.
Clearly we can see the intent of the designers here. When you look at
Intimidate's game text compared to SoS, you can see that the wording of the card in no way indicates that the exertion is prevented. In fact, the phrase "place no token for that exertion" explicitly indicates that there is, in fact, an exertion that takes place even after you resolve the effect of the card.
Intimidate, on the other hand, clearly
prevents the wound from happening. So any FP card that has a cost of "wound a companion" would be nullified if you used
Intimidate, because it prevents the cost from being paid.
Because SoS does not explicitly prevent an exertion, but modifies the conditions by which an exertion happens, I argue that effects that require an exertion as part of their cost are not prevented by SoS.
I believe there was a rules clarification that Mark Tuttle put out on this card that illustrates this very point. I'll see if I can find it in the Internet archives.