Ring famous baseball player in NY team after hospital produces unpleasant facts (4,6)

I believe the answer is:

home truths

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'facts' is the definition.
(I have seen 'harsh facts' mean 'home truths' so perhaps 'facts' could also mean 'home truths')

I cannot understand how the remainder of the clue works.

Can you help me to learn more?

(Other definitions for home truths that I've seen before include "Unpleasant facts told to person about himself" , "revealing facts about writer" , "Hotter mush (anag.)" , "harsh facts" .)

I've seen this clue in The Telegraph.

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