Well, there can be some truth to this cruise assumption, so maybe it's not entirely a myth. There is plenty (and I do mean plenty) to eat on a cruise. If you go in with the mindset that you want to get the most for your money, even if that means eating until you explode (or at least suffer gastrointestinal distress), then yes, you may very well gain 5 pounds in the week you're on board.
However, this is not a requirement.
Today's cruise ships have changed with the changing attitudes of many health conscious vacation goers. There are food options for everyone. Yes, you can get the French fries and deep-friend chicken sticks, but there are also lighter portions of healthier foods, including vegetarian options.
Also cruise ships have lots to do besides eating, and all of the large, mainstream ships have fitness centers. Expect weight rooms, fitness classes such as yoga or pilates, and lots of cardio machines such as treadmills all available for your use 24 hours a day.
Also, just about all ports you visit offer shore excursions for the physically active. You can go for hikes, go kayaking, go mountain biking, or sign up for a horseback riding adventure.
If staying in shape is important to you, it's absolutely something you can do while on your vacation. In fact, you'll have lots of time for physical activities since you won't be at work!