Cobra, is this behavior happening on your iFly device or tablet, and what software version are you on. This was addressed some time back. I can't duplicate your reported behavior of KDTN not being recognized as an airport.
I just tested on my iPad and V9 on my box and if I enter KDTN on the Flight Plan page it adds "[KDTN] Shreveport Downtown" immediately to the plan. If I enter DTN, I get an option of the VOR or APT, but only if I have the VORs checked on the search page. If I don't, it immediately adds "[KDTN] Shreveport Downtown". If you don't want like identifier VORs listed as an option, just uncheck the VORs box.
If I try the same for KTKI or TKI, I get the airport added immediately, as there is no like named VOR to conflict with it. This seems like the proper behavior you and Tinker described you want. The only difference is that we will all entering a three letter airport to be entered if there are no like Navaids. Lots of iFlyers are used to this behavior and would probably create unnecessary frustration to pull that out when it's not a functionality flaw.