There's two ways to look at this. One, is that the FO is simply ignoring the injury history in hopes that the ppl layer stays healthy and the upside of a deal pans out. The second is to recognize that players like this tend to come cheaper and yet still pose some upside should they stay, or even while, they stay healthy. Either way, they're trying to capitalize on upside. Given that many of these deals, particularly with pitchers, are short term deals they're trying to maximize the potential of catching lightning in a bottle while also minimizing long term risk.
Some of the players listed here don't really fit into this conversation, in my opinion. There's always a risk for players to get injured. It's exceedingly rare that a player has a long career without so injuries.
I'm not sure I completely agree with the FO's approach on injury prone players, but I also don't think they're as careless about it as some suggest.