Mostly an old wive's tale. As with any brass you should weight at least a sample of them to check to see how they compare to others. I do not recommend mixing headstamps in bottle neck rifle rounds due both to accuracy problems and potential pressure problems it can create.
Even with commercial brass you can easily find 10-15 or more grains difference between brands and some times even with same headstamp but different lots. Based on my experience with LC brass I'd not expect them to be much if any heavier than most commercial brass and perhaps even lighter than some brands.