Could a person have contracted the disease from rinsing water left in the sink too long?
Alternatively, could the person have contracted the disease by drinking water from a water tank which has three filters and then put in a water purifier?
Possibly, yes. Fresh tap water may also contain Legionella.
Concerning the water tank, if the filters are designed to catch bacteria and the purifier can kill bacteria, these may be effective in keeping the water pure. Many filters and purifiers are unable to stop bacterial contamination. You have to read the fine print on the product.