The SEC rules if you're in the US are quite strict. You likely wouldn't be able to do quantitative trading own your own while working at a quant. Though, it might help you get hired as a modeler.
Sell-side bank like JPMorgan, HSBC, then yes you are correct.
Buy-side hedge fund or prop shop, no you are wrong. The SEC/CFTC does not care what you trade in your personal account.
Sure you can still trade of course. but you might need things like preauthorization for every trade, and have to hold them for a given time before selling, which kinda makes algorithmic trading more difficult.
But hey ya'll just pile on. o/