Training with weights does not make you slower, and referencing a single 30 year old study that nobody can find probably indicates what modern exercise science already tells us.
Training with weights, or in water, does not reprogram your brain at all, unless your martial arts training is bad (which is probably the case for most people who don't train realistically.
Watch this video, and try to defend the idea that "leg day" makes people slower. It's an argument from absurdity. We don't need to track down some old study from the late 90's, but if we did and you tried showing it to a fight coach, they'd probably think you were trolling them.
Pay special attention to that part at about 1:00 in when he says about "isolate and do it slow". This is one of the best coaches on the planet, blowing apart the notion that training against water, in water, or with resistance, including body weight, does anything negative. If anything, doing these things makes you faster, stronger, and more powerful.