Yes, they cannot dock your pay below the minimum wage. Same as they must pay you minimum wage if you don't meet it with tips. Nobody with a tipped minimum wage is getting paid less than the federal/state minimum wage applicable to them.
So if you work 40 hours in a pay period, and minimum wage is (for argument's sake), $10/hr, you will not make less than $400 when any deductions or tips are taken into account. If your tipped hourly wage was $5/hr, but you only made $100 in tips, that'd be 40hr * $5 = $200 + $100 tips = $300. Your employer would have to add $100 to your paycheck to ensure you made minimum wage.
In the same vein, if you had made $300 in tips, and your total pay was $500 that pay period, they could theoretically dock your pay up to $100, so that you meet minimum wage, but not below that.
In practice, very little to no employers are ever going to dock pay for something like a dine and dash as it's just too messy and definitely not worth entertaining any potential legal challenges. It's hardly what most "most places" do. ERA loves to misrepresent the shit out of stuff like this.
Tipped employees also virtually never end up making below minimum wage after tips (and are often well above minimum wage), so the employer matching to minimum wage almost never comes up, but is the law and only the most reckless of establishment would be brazen enough to ignore this law, or a rogue shitty manager.
Sorry, sounds like you have a shit manager. I've voided plenty of mistakes, dine and dashes, etc. I've also caught employees defrauding the restaurant by retroactively and systemically adding discounts (like the employee discount) to cash orders then pocketing the difference ¯\_(ツ)_/¯ Hardly means everyone does it.