But I'm guessing that for an inspection they are just looking at visual things like vegetation changes, low spots, etc. The lack of extensions on the downspouts is a big no-no in sinkhole country. (Well - anywhere really).
I wonder if the guy is like me and a little bit lazy on maintenance and stuff. Could be he saw a depression getting worse in the backyard and didn't know the danger, and was thinking “I'll get around to filling it in some day”.
Noticed on street view of the house there is a storm drain to the left of their mailbox. Would be worth looking into to make sure this drain is functioning properly.