Hull's accounts - released last week, five months behind schedule - showed borrowings of £22million, prompting accountants Deloitte to predict the Tigers will have to raise £23million to balance their books should they be relegated, and £16million if they survive.
But Pearson told the Hull Daily Mail: "If I felt the club was in imminent danger I'd have thought long and hard about coming back. Every problem at this club is solvable and the supporters should rest assured the club is in no danger of going out of business or going into administration."
Pearson also lifted the lid on the deal which saw Turner join Sunderland in August for what was described at the time as an undisclosed fee.
Tigers manager Phil Brown had previously valued Turner at around £12 million but it has been revealed the 25-year-old cost the Wearsiders just £4m.
The deal does not include any add-ons based on performances with 33% of the £4m going to Turner's former clubs Brentford and Charlton.
The size of the fee has again raised questions about the necessity to balance the books but Pearson insists the club didn't have to sell, adding: "Under no circumstances was it a financial necessity to sell Michael Turner.
"I can only second guess what people were thinking but there was probably a feeling the player wanted to go and that was the best possible deal available for him.
"It's not incremental, the total amount of cash we will receive for Michael Turner is £2.8m. Those are the facts."