My first broker taught me that if a buyer states that "money is no object", that literally, money is probably not an object that they posess. I think the same logic could easily apply here.
However, there is a different side to it - because pre-qual and pre-approval letters have specific dollar amounts stated, a buyer might be hesitant to show their cards, i.e. inform the seller that they can afford 1.25X when the offer is X. If that's the case, then the buyer should be willing to produce the name and phone number of his banker, who would (with the buyer's permission) be able to verify that the buyer is qualified.