I don’t buy into that. There’s a difference in pushing the bully back assertively without necessarily stooping to their level.
Nobody is advocating we attempt to cheat like Republicans, for instance (at least I hope that wasn’t what was meant by fighting dirty). Just stop coddling them and pretending they’re acting in good faith when clearly they are not. I’ve seen more of this assertiveness come out over the years from Democrats and it’s long past due and could be tripled easily.