Make sure you ask the right question, "does the ladder crew search a building with or without a hose line"? I don't know how you got RIC in there, that is not what we were talking about. We are talking about fire attack and simultaneous search for trapped citizens. Engine doing the fire attack and ladder doing search, hose or no hose for the search team?
We aren't properly trained because we enter without a hose line? You sound ridiculous. Look at an article just posted on here about the 3 rescues my department made last night in Washington, DC. All made by Rescue 2. Not one of them had a hose line. Instead of saying we aren't properly trained, I would actually say we are better trained. If you know what you are doing then it shouldn't be a problem.
I suppose "always" has a different meaning in the fire service! ;) You always do what you have to. If the building is untenable, then there are different calls to be made of course, but you always try.
My point was, it should be practice to always take a handline in to the structure, what happens if the only way to the victim is through the fire? So many what if's in this business, but it is Best Practice, to Always take a handline! :)