No, it's not true.
According to this article in Scientific American, there is a slight additional energy required to start up a fluorescent bulb, but it lasts an extremely brief time:
that power surge is so brief that its energy draw doesn't amount to much: the equivalent of a few seconds or so of normal operation, according to U.S. Department of Energy estimates.
The article recognizes that there is some additional wear-and-tear each time the lamp is turned on, which may have an impact on life. It recommends turning them off if you won't need them for more than five minutes.
A simple rule of thumb that balances both concerns is to shut off fluorescents if you’re planning to leave a room for more than five minutes, according to Francis Rubinstein, a staff scientist in the Building Technologies Department at Lawrence Berkeley National Laboratory's Environmental Energy Technologies Division.
The above article is directed primarily at CFL bulbs, but here is a reference from the California Energy Commission based on more conventional tubular fluorescent bulbs. It comes to the same conclusion, stating
The modern electronic ballast and T8/T5 lamp combination do draw a higher level of current during startup, but it only lasts for a fraction of a second, which is negligible compared to normal current requirements of the lamps.
Their recommendation is the same:
You should turn off your fluorescent lamps if the space is not going to be occupied for more than a few minutes (3-5 minutes is a good rule of thumb)