This is a story that is often told, but is poorly documented. The history section of the Lamborghini web site acknowledges that Ferruccio Lamborghini entered the high end sports car market in 1963, with the express intent of competing directly with Ferrari. It does not make any mention that Enzo Ferrari insulted Ferruccio Lamborghini. However, I have read many books about my favorite sport, Formula 1 auto racing. This story was told, in passing, in at least six books about Formula 1 racing that I have read during the last ten years. Unfortunately, in the two books I have on hand, right now, this story is not mentioned. Basically, there is not enough evidence to convict anybody of slander.
Enzo Ferrari started to produce high end sports cars in 1949, which were sold at astronomical prices to fund the Ferrari racing team. Enzo Ferrari also has a notorious reputation of treating his customers like crap. He was very brusk with his wealthy customers. He did not have the time to deal with people who just wanted to bask in his reflected glory. Enzo Ferrari was to short tempered to respond constructively to any customer that complained about their Ferrari road car. It probably happened, but I can't prove it happened, with enough evidence to stand up in court.
This is an old trope in the automobile industry. It goes as far back as 1898, when James Ward Packard bought the tenth car built by Alexander Winton. Packard complained about the short comings of the Winton, which was an early leader in the automobile industry. Alexander Winton was a hot tempered Scot and he challenged James Ward Packard to do better. Packard went on to start the most successful luxury car brand in the first half of the 20th century, while Winton began to decline after 1915 and exited the automobile industry in 1924. This incident is well documented in the corporate histories of both Winton and Packard, but the alleged Ferrari / Lamborghini is confrontation is notably absent in the "official" histories of both Italian sports car companies.