No it's not true. It won't cause it to fail, not immediately anyway.
SSDs have firmware which balances the writes to different NAND memory cells in the drive, so the wear on these cells is levelled. Effectively it is fragmenting your files across the cells.
You can defrag your drive, but there is no point, the firmware will just move it around again - and you've added unnecessary wear in the process.
The main problem with SSDs is degradation in performance as cells are written, then freed up they are in a dirty state and need cleaning to get back to original performance. Tools exist for some of the drives and TRIM will do this automatically once the OS (Windows 7 supports it), the drive and the SATA/RAID drivers all support it.
Yes SSDs have a finite lifespan, once the cells have been written so many times they will be marked bad and the drive will start to lose capacity. Warranties on the drives are generally around 3 years, with some longer and have a MTBF similar to mechanical HDs.
Unless you plan on keeping an SSD a very long time, or have a very demanding use for them then failure due to them wearing out should not be an issue (though I do accept it's maybe too early to know how long they will truly last for home use/enthusiast use).
