Periplaneta americana came from Africa. Most of the other roaches in Florida came from South and Central America. (Pycnoscelus surinamensis, Panchlora nivea) Periplaneta australasiae came from... Well, you know .
The funny thing about the article is the dishfuls of errors it has; Lizards will eat anything, (just because they will, doesn't mean they should) roaches will infest houses, (the day Blaptica dubia infests a house is the day I die) and, to top it off, the statement that it's illegal to import roaches into Florida. (Only Gromphadorhina portentosa, no other species; not even its cousins who share the same genus name.) Besides, the worst another species of cockroach could do is... Eat some more dead leaves. Just like all the other Florida roaches do...