In summary: typical pass-through entity distributions are typically taxed as self-employment income and subject to the SET which attempts to recover the missing employer's half of tax payments. You cannot avoid all employer's half of taxes by taking them as distributions, and whomever told you that has misled you.
Now, what you might actually be thinking here, and would be correct, is that for those who earn less than a certain income (which would place them in the top tax bracket), the effect of applying all of those payments as self-employment income generally results in a lower tax rate than the corporate tax rate, and allows for deductions that companies may not have available to them.
What you're talking about does not apply to LLCs, it is a special situation only related to S-Corps. Generally speaking, pass-throughs such as LLCs all distributions are taxed as self-employment wages, except under certain conditions.