Apologize

"I'm sorry your dad passed away."
When you hear somebody say the above to you, would you describe what he said as "He apologized for my loss"? I guess you don't use "apologize" for something you are not responsible for.
What caused me to put up this query is the following passage:

Wedged in the door frame of our house, I found the business card of a lawyer named William Benjamin; on the back, he claimed to represent my dad. With phone service disconnected, I called from the neighbor's house and was surprised when he showed up at the house early the following morning, briefcase in hand.
I led him inside the dim house, and he took a seat on the couch. His suit must have cost more than I earned in two months. After introducing himself and apologizing for my loss, he leaned forward.
"I'm here because I liked your dad," he said. "He was one of my first clients, so there's no charge for this, by the way. .... "

The author, stationed in Germany, away from home, lost his dad, who had been in an extended care facility, and came back on an emergency leave. What do you think "apologizing for my loss" mean?
Thanks in advance for your help.
Hiro/ Sendai, Japan