What you've been told is for the most part true. Due to the constant movement of soldiers into and out of the base, creating a lot of competition in listings, and the fact that most of the buyers in our area are soldiers using their VA, with no money down, it's very common for the sellers to pay the buyers' closing costs. You don't have to, but most of the other homes in the area will.
Since your tenant is already living in the home, and will incur moving costs if choosing to buy another home, that might be a factor in how much in closing costs you offer to pay. However, refusing to pay any costs may spur your tenant into purchasing another home. It's a gamble! The rental market is strong in the Killeen area, so chances are good you'll find another renter, but you never know how that will go either.
Bottom line, if you're ready to sell, it's probably a good idea to pay at least a portion of the buyers closing costs and sell to your tenant. If you're not ready, then don't sell, and possibly take a chance on another tenant.
If you'd like a market analysis and a more personalized look at the market in your specific neighborhood, let me know! I'd be happy to help.