A lot of people use excuses like these when they give up their animals because they can't afford medical treatments or they don't want to get involved with a sick dog or there are behavior problems that they either aren't capable of dealing with or flat out don't want to deal with. We see it more times than you can imagine. That is NOT to say that everyone who surrenders lies, but you would be surprised at how many do.
The woman that I got Abby from told me that she had to give her up because her daughter was allergic to her. But now we know that Abby was in kidney failure and that just didn't want a sick dog in the house. Judging by the price I paid her for Abby, I'm pretty sure she wanted to recoup some of her money too.
Please don't take offense at @kazzy220's statement but don't take a persons honesty or integrity for granted either.