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No this is not true at all. There is only a slightly higher cost for wireless than wired.
A wireless cards range from $10 - $20 each, and a wireless access point can be purchased for less than $50. You will still need all of the wired infrastructure, routers, switches, etc.. to run the wireless.
The disadvantages of wireless are speed, security, and range.
For speed, the best you can get is 802.11N these days, which is 300Mbps, where with wired LAN
you can get speeds upto 1Gbps if you have the hardware to support it.
For security, while wirless encryption has come a long way since the early days of wireless,it is still not fool proof. The security is much better with wired.
Range, wireless has limited range, so you will need to have many access points to cover a large facility, or you may only have connectivity in certain areas. Wired connections are static, that is you must be plugged into it to use it, but you can have many more wired connections availible within a given range from the servers. So for range, there are both advantages and disadvantages to wireless