Its a lot harder to kill yourself (or another person that is actively resisting) with a knife than with a gun. Having been in barroom brawls where knifes came out I can tell you that with certainty.
People that kill themselves by cutting themselves typically have to do a lot to make it work (for example preparing a hot bath to prevent clotting, etc.). And they need to cut deep, and cut correctly (slashing up and down the wrist, not across for example, as typically shown in movies) to achieve the goal, which is rather painful unless again one takes the time to acquire pain medication and consume it. This increased preparation time increases the mental barrier one needs to overcome to order to actually complete the suicide attempt and the increased time required to perform the act makes it more likely that someone might catch you in the act and save you.
People also tend to kill themselves in private, in their home, where they can't be interrupted and have had a lengthy time of isolation to deepen their depression. A handgun in the bedroom drawer "just in case" is a very easy way to attempt suicide and is in the ideal, private and quiet location that most people seek when trying to kill themselves. Other means that people choose in private, such as hanging themselves, typically have large mental barriers to overcome. Its not easy to correctly form the type of noose one needs, for example and also the death itself (by a possible lengthy suffocation) is a scary barrier to overcome. One must be very depressed to overcome that, and often when someone is that depressed they are not capable of the work involved to make it happen (and also there is a bigger chance for another person to notice how depressed they are, and offer help).
Although it is easy to crash a car as you mention, typically this is not what people want to do to kill themselves (typically, but yes there are always going to be outliers). As pointed out most people seek privacy and a period of isolation. Driving on the highway at speeds enough to cause death is not private nor isolated. And bridges can be better secured such as to make it harder (using fencing for example) and we can place emergency help phones on the bridge as well, which have been known to save people by giving them a person to speak with when they need it most.
The study is suggesting that people when deprived of an easy, private death in the convenience of their own home act on suicide impulses a lot less simple because its harder to do in the conditions one typically seeks.
