This has.not been true for more than 30 years. Veneto is the heartland of the original Benetton, a heavily industrialised region, the engine of the Italian North-East economic mini-boom of the 80s/90s (based on low-cost manufacturing). In fact, there is a massive duality between the tourism industry in Venice and the economy of the mainland, which is markedly reflected in politics (Venice tends to elect leftist mayors, while Veneto as a whole is very rightwing).

Losing the tourism industry would definitely be a blow to the economy, but Veneto would survive economically just fine.