Calling to request a new phone bill

After telling the operator on the other end my name, she asks,
"Gonin sama desuka?" (五人様ですか？ Are there five of you?)
I, not really understanding what she said nor why she would ask if there was five of us, but reasoning that she might think it's the family who lived here before me (it'd happened before with phone companies), say,
"Iya, hitori desu kedo..." (いや、一人ですけど・・・ No, there's just one of me...)
Suddenly a burst of natural, high-pitched laughter comes from the other end of the line,
"Iya, iya, sore janakute, honnin-sama desuka?" (いやいや、それじゃなくて、本人様ですか？ No, no, no, is this the customer speaking right now?)
OH! Hahahahaha! The burst turns into a flow of laughter as any of the nervousness or tenseness from me having a little bit of trouble ordering a replacement bill over the phone in Japanese melts away. We laugh together for quite a long, loud while. I feel like the two of us have achieved something very special and rare in (this) society - between two strangers, a sudden, instant sharing of an intimate experience, akin to that of two good friends. I tell her that yes, it is me, I am the customer. Hahaha, we keep laughing throughout the whole rest of the conversation to the very end. That was a unique feeling of connection with someone I don't even know, never saw face-to-face, and will most likely never meet again. Hahaha!