That is not really true, or at least the idea of what a salary cap would accomplish changed from what the NFLPA might have had in mind originally to what was finally agreed upon in the 1993 agreement. Remember that the NFLPA wanted free agency, and a salary cap may have been hoped to act as a ceiling on teams that would force player movement. I honestly don't know who first proposed a cap.
After the league was ruled by the courts of being insulated from any anti-trust action based on the mere existance of there being union representation during the impasse, the NFLPA had no recourse but to decertify. This effectively removed any insulation the league had from anti-trust law. Realizing this, the league came up with Plan B for free agency that basically opened up free agency to 10 players per team to attempt to try and protect itself, but a group of players filed an anti-trust suit against the leagues plan B and the league lost that battle in court after a jury found it to be too restrictive to the players. Instead of appealing the decision, the ownership initiated a new round of negotiations and eventually settled on an agreement with the union that opened up free agency to basically what it is today in exchange for a salary cap that would protect them from excessive spending. The NFLPA may have been the first to propose a cap - possibly back in 1987 before the strike. I don't know. But what was agreed upon by the time 1993 came around was a compromise solution to offset the union's gains in free agency, and this has favoured the ownership - particularely as the agreement coincided with a number of huge renewed TV deals in the early 90's around the time of the new agreement. Increased revenues and capped expenses ( outside of the signing bonus loop-hole ). Not to say that the players haven't benefited from the agreement, but if I were an owner - that would put a smile on my face. No matter who proposed it first.