I honestly dont know the answer to your question but have seen similar.
I checked a site from a competitor using the site: function with that showed no results but if i search for the web domain i get 800+ results.
Semrush shows 700+ keywords but 0 traffic (expected) since 2012
I checked when google last crawled this site and it just shows -- rather than a date (free guesstimator)
I then checked to see if the site was penalized or sandboxed and result was probably, i checked penguin penalty ( or some such) and the graph showed the site had been growing but started to loose traffic just before penguin was released after which it never recovered.
What i personally think is weird (more experienced people may shed some light on this) is that the site is ranked #1 for a certain keyword compared to other sites who are specialists for this keyword (its an occupation, which this guy isnt but has one reference to it ) and are not penalized by google, there are no backlinks or anchor text for this keyword and no pbn yet the site still ranks for alot of keywords yet not included on the site: function, the site is over 10 years old but its so basic and has very little content yet is able to rank.
Go figure
Regards,
Venturi