I agree with Connie. There is of yet no documentary evidence that firmly connects William H. to Timothy and Hannah (Bishop). However, the basics of name, date and place, especially place, points to Timothy and Hannah being William's parents.
The 1820 census for Seekonk, Bristol Co., MA has one male 10-15 (probably William), one male 45+ (Timothy) and one female 16-25 (probably Timothy,s daughter, Olive).
The 1830 census, also for Seekonk, has one male 20-30 (William H.), one male under 5 (probably his son, James H.) and one female 20-30 (probably his wife, Almira).
In 1840 William is enumerated in New Providence, Providence Co., RI. There are one male under 5 (unknown), one male 10-15 (James H.), one male 30-40 (William H.), one female 30-40 (Almira), and one female 60-70 (probably the Dorothy Fisher who appears, age 72, in 1850).
Thus we can see that all this takes place near the MA and RI border, relatively far away from Long Island, NY where Michael Titus came from.
The Attleborough Marriage records has the marriage of Almira B. Fisher, unmarried, of Attleborough, and William H. Titus of Seekonk (note the place), on Nov. 20, 1825.
I have a William Henry Titus, son of Timothy, born Jun. 29, 1804 at Rehoboth, Bristol Co., MA.
Sometimes we have to go with what we have, and in this case I'd bet on William Henry being Timothy's son. However, don't stop searching for the proof.