Manchester police chief Michael Todd did not have a "huge" amount of alcohol in his blood when he died on Snowdon, the coroner said as his inquest began.
The body of Mr Todd, 50, contained 105 milligrams of alcohol per 100 millilitres of blood - above the legal limit for driving of 80 milligrams.
The coroner said he was hearing medical evidence to dispel misleading reports.
Meanwhile, Mr Todd's widow Carolyn paid tribute to "a caring and loving father and husband".
The findings on alcohol were made public by consultant pathologist Dr Anthony Caslin, who conducted the post-mortem examination on Wednesday at Ysbyty Gwynedd Hospital in North Wales.
After the details of blood tests were revealed, the coroner, Dewi Pritchard-Jones, asked him: "So, not a huge amount of alcohol then?"
Dr Caslin answered: "No, sir."
There were no injuries on the body, and Mr Todd was fully, although lightly, clothed when found on Snowdon, the inquest at Llangefni, Anglesey, heard.
As questions remained over his death, Manchester's Chamber of Commerce said it supported its boss Angie Robinson, following reports that she had been having an affair with Mr Todd.
Mr Todd's widow said she and their three children were "struggling to come to terms" with his death.
Her statement said: "I loved Michael very much and the last time I spoke to him he told me he loved me too."
The inquest, which has yet to establish the cause of Mr Todd's death, was opened and adjourned on Thursday.
Angie Robinson is alleged to have had an affair with Mr Todd
No date was set for the full inquest.
Mr Pritchard-Jones was told that Mr Todd fully clothed but the garments were only light. There were no external or internal injuries.
The coroner said: "There was no evidence this man had jumped from height or sustained any significant injuries."
He said releasing the medical information about Mr Todd was necessary to "allay suspicion and fears".
"We are hearing this evidence today to get rid of some of the ridiculous stories I have read in the papers and had put to me over the last day," he said.
Mr Todd had been married for more than 27 years and had three children - a 16-year-old daughter and twin boys aged 13.
The chief executive of the Greater Manchester Chamber of Commerce, Angie Robinson, was offered the support of the organisation's chairman after reports relating to her alleged relationship with Mr Todd.
In a statement, Peter Heginbotham offered Mrs Robinson ''our full support'' after details of the alleged affair emerged.
The statement said: "Angie Robinson is unavailable for comment today.
"However, she has the full support of the chamber in her role as chief executive."
Mr Todd lived in a flat in Manchester city centre and returned to his wife and family at their house in Nottinghamshire at weekends.
The BBC has learned he suffered from bouts of depression and had previously threatened suicide.
In the hours before he died, he sent a series of "worrying" text messages to various people, which caused concern for their safety and his own.
BBC home affairs correspondent Daniel Sandford said the investigation may focus on Mr Todd's distressed state of mind and what support he had been given by Greater Manchester Police.
Books of condolence have been opened at Manchester Cathedral and online at the Greater Manchester Police website.