A little exaggeration but not much. There were 234 commissioned ships (including submarines) in the Navy as per the US Naval Register, current as of 31 December 2016 . There are 223 active duty Admirals (O7-O10) now. That includes 162 Admirals assigned to the Navy plus 61 more Admirals assigned to joint billets as of 2016. This number comes from the 2016 report at the link below and does not include reserve component Admirals. The number of active duty Admirals has been reduced significantly since 2012 so I am not certain that it was an exaggeration in the past.
https://fas.org/sgp/crs/natsec/R44389.pdf
https://en.wikipedia.org/wiki/List_of_current_ships_of_the_United_States_Navy
Thanks, I've seen various numbers, not sure which ones should apply:
"The United States Navy has over 440 ships in both active service and the reserve fleet, with approximately 70 more in either the planning stages or under construction, according to the Naval Vessel Register and published reports."
Of those, as you posted, just 234 are "commissioned", the rest non-commissioned (105), ready-reserve (51) and other support ships (50).
Non-commissioned ships include such as USNS Spearhead class, and Mercy class hospital ships:
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