The same book that categories the giant spider sighting in Milan also has one about a large spider that attacks birds in the Caribbean islands and the southern USA just underneath it. It says that the spider's body is at least one and a half inches long, or bigger. This implies that the spider has a very, very large leg span.
You may say that the spider is the Goliath Birdeater, however this is wrong as the Goliath is only native to the Guyana region and some parts of northern Brazil. Therefore, it cannot be this.
The next likely suspect is the Huntsman spider, the only other spider of comparable size to the book's creature, that also happens to live in the southern US and Caribbean islands. Well, this is likely as the book describes it as moving fast, attacking birds and lizards, and hiding in nooks and crannies, just like the Huntsman in real life.
This does not debunk the myth though, in fact it makes it even more powerful. As seen here, a good comparison to a fully grown, adult Huntsman is about the size of a US penny. A US penny is less than an inch in total. Therefore, the mythical spider mentioned would need to be at least twice as large as a normal Huntsman.
Spiders of this size actually live in Laos, Vietnam and other south Asian states. This means that they would be nowhere near the Caribbean or Florida.
Vice City and Florida both exist at the same time (as seen in the Move Over Miami billboards in Little Haiti.) With the inclusion of the Gator Keys initially, it implies that Vice City is located somewhere near the Florida mainland and the Caribbean sea. It just so happens that Huntsman spiders live in Texas, Florida and the Caribbean.
It is possible that the giant spider in Vice City is just a very large huntsman, and not the mythical creature mentioned in Milan.