Let's take the most likely to occur scenario, dealt 4 to the royal and fill on all 3 lines.
P(dealt 4 to the royal) = 1 in 2700 ( approximately)
p( fill in royal on 3 lines) = 1/47 1/47 * 1/47 = 1 in 103823.
P(dealt 4 to the royal) * p( fill in royal on 3 lines) = 1 in 280 million ( about). Now, this is 280 million dealt hands, which is 840 million played hands at triple play.
This is the most likely 'royal on each line, not dealt' possibility. I think they should pay you the progressive.