Yes, this was suggested in Venice on the tour when I took it as well. Most of the people followed the suggestion. It was not a suggestion for Cinque Terre at that time although we were told about the train ride and the difficulty of luggage handling.
Depending on how much luggage you have, it might not make a difference. If you are traveling light as also suggested with a single carry on, you can probably get by taking everything with you. However, the walks in Venice can be long over cobbled walkways and up and down lots of steps over the bridges. It is not friendly to wheeled bags. It is not friendly if you cannot cary the bag without using the wheels. Even if you just leave your dirty clothes in the bus it can make the walk more enjoyable with a lighter bag. In Cinque Terre they had the hotels meet us with trucks for the luggage and it was waiting in the hotel when we got done with our orientation walk. After dealing with the luggage on and off the train, I would suggest leaving what you can on the bus in Cinque Terre as well, especially if you end up at one of the hotels up the hill side.
I don't know where the bus was parked in either location, but it was a long way from where we were. I'm sure it is in a secure place or they would not suggest leaving things. The things you leave are in the locked underneath baggage areas, not in the seating area, so no visual enticement for any passing criminal. They are not suggesting you leave your electronics or anything else of higher value, just excess clothing or other things you won't need during that stop. And make sure any medications you need are NOT left on the bus at either location. You will not be able to get them until the next bus day.
