I am not a lawyer, but I am literate and I know how to google. As such, I know that there exists a public document called Utah Code, Title 41, Chapter 6a, Section 1105, better known as The Law which is implicitly referenced. The irony is that I can use the same section literally as a succinct edict that might elicit a practically opposite interpretation: "a person riding two abreast with another person may not impede the normal and reasonable movement of traffic and shall ride within a single lane." In reality, this section of the law is quite a bit more complicated, and as always, the letter of the law is distinct from its interpretation and application in court.
That said, there are several other obvious ways to interpret taking a lane as legally condoned; personally, it seems to dictate that I should take a lane any time I deem it necessary to ride safely, which is to say, in accordance with the notion of vehicular cycling, Always.
At best, these billboards are wrong. At worst, they are an indication of the sad state of our governance--is it really acceptable to substitute enforcement with inaccurate, passive advertisement? If it is, why don't we see more billboards describing all the other ignored laws? Consider this gem (section 907): "Vehicles emerging from alleys, buildings, private roads, or driveways must stop prior to sidewalk area or street."
The best way to battle ignorance is to learn for yourself and to teach others. To this end, look at some of the other bicycle relevant laws after the jump. Despite what we may come to know as the truth, it seems that until those billboards are torn down and their message fades from memory, the best we can do is lament the greater than usual amount of ignorance spewing from car windows.
As found in the Utah Code, Title 41, Chapter 6a
41-6a-706.5 Operation of motor vehicle near bicycle prohibited.
41-6a-1102 Bicycle and device propelled by human power and moped riders subject to chapter -- Exception. Highlight: "A person operating a nonmotorized bicycle or a vehicle or device propelled by human power is not subject to the penalties related to operator licenses under alcohol and drug-related traffic offenses."
41-6a-1103 Carrying more persons than design permits prohibited -- Exception.
41-6a-1104 Persons on bicycles, mopeds, skates, and sleds not to attach to moving vehicles -- Exception.
41-6a-1105 Operation of bicycle or moped on and use of roadway -- Duties, prohibitions.
41-6a-1106 Bicycles and human powered vehicle or device to yield right-of-way to pedestrians on sidewalks, paths, or trails -- Uses prohibited -- Negligent collision prohibited -- Speed restrictions -- Rights and duties same as pedestrians.
41-6a-1107 Bicycles -- Parking on sidewalk, roadway -- Prohibitions.
41-6a-1108 Bicycles and mopeds -- Turns -- Designated lanes.
41-6a-1109 Bicycles and mopeds -- Turn signals -- Exceptions.
41-6a-1110 Bicycle and moped inspections -- At request of officer.
41-6a-1111 Bicycle racing -- When approved -- Prohibitions -- Exceptions -- Authorized exemptions from traffic laws.
41-6a-1112 Bicycles and mopeds -- Carrying bundle -- One hand on handlebars.
41-6a-1113 Bicycle -- Prohibited equipment -- Brakes required.
41-6a-1114 Bicycles -- Lamps and reflective material required.
For Salt Lake City, bicycle specific laws (very similar to those of the state) are found in chapter 12.80.
A printable summary of these laws can be found in a .PDF provided by the city here.
Rules for the University of Utah campus can be found in the Utah Administrative Code:
Rule R805-1. Operating Regulations for Bicycles, Skateboards and Scooters.