First a question. If you have absolutely no reason to doubt them, then why are you? Do you doubt their honesty? Why?
As for resources, as Grande stated, you could simply ask them where they get it from.
Otherwise, depending on your location, there are a limited number of fresh seafood distributors in a given area so it's not like you have to investigate a large number of possibilities. Unless you are in a coastal area, they are most likely getting it from one or two possibilities.
A quick google search will provide a great deal of information on the many issues of sustainability facing our seafood supply.
A result of all this is that reputable suppliers are very aware of concerns like yours. They share them. So while there are a number of factors involved in sourcing salmon, tracking sources has become a big part of the entire industry. Not only have laws been passed to insure proper labeling and identification, the suppliers are keenly interested in promoting themselves as purveyors of sustainable fishing practices.
Looking at the broader picture, there have been many studies and investigations into what the fish you buy and eat is called versus what it actually is. When fish are found not to be what they are sold as, identifying where the mislabeling occurred is much harder the more middlemen are involved. This is much more common with fish of similar appearance and texture, where one white fleshed fish looks much like another. So while the seafood and food service industries in general continue to have issues about proper identification of many fish, salmon, because of it's distinctive appearance and taste is much more easily identifiable to begin with and more easily tracked as a result.
In a nutshell, salmon fishermen these days want people to know how special their wild salmon is. Salmon suppliers want the consumers to know they are supplying that special salmon. So while the possibility exists that the store you frequent may be selling farm raised salmon, if they tell you it's wild, it is because they have every reason to believe it is. And if you ask them where they get it from, they will most likely be very happy to tell you.