This is NOT true. For all fission reactions, the number of neutrons can change. U-235 can fission and, besides the fission products, result in only two other neutrons or even more than three, but rarely. There are also differences in when neutrons are emitted - the different cases are called prompt neutrons and delayed neutrons.
As theCandyman already mentioned, the main fissile isotopes of U and Pu release either 2 or 3 neutrons from each fission.
The average number of neutrons released by each thermal fission is:
2.49 for U-233
2.42 for U-235
2.87 for Pu-239, and
2.93 for Pu-241.
As the neutron energy increases, the average number of neutrons emitted per fission increases, but the probability that a neutron will cause fission, rather than simply being captured, decreases with increasing energy.
These and other heavier nuclei can also undergo spontaeous fission but at very low rates.
Some fission products, e.g. Kr-87*, a decay product of Br-87. Kr-87* is an excited state of Kr-87 and emits a single neutron. The delay is based on the half-life of the precursor Br-87. There are several groups of delayed neutron precursors and this delay allows for control of nuclear reactors.
This might be of interest -