Pitman is trying to lay claim to having netted twice in Saturday's 2-0 win over Accrington a feat that would see him become only the third player in the past 38 years to hit 20 league goals in a season.
However, standing between Pitman and the chance to join James Hayter and Colin Clarke in the Dean Court hall of fame is team-mate Liam Feeney, who also wants one of the goals.
Feeney appeared to have opened the scoring for Cherries when he beat goalkeeper Ian Dunbavin with a right-foot shot in the 18th minute, the goal credited to him by every media source, both local and national.
But after grabbing Cherries' second 11 minutes from time, Pitman was at pains to point out that he had applied the final touch to Feeney's strike and was adamant the goal should be his.
Cherries' leading marksman had a key witness in referee Graham Scott who later confirmed to the Daily Echo that he would be notifying the Football League of a Pitman double.
When contacted by the Echo, a spokesman for the league said the Press Association's verdict that Feeney had scored would be cast in stone, unless Cherries challenged the call.
And Cherries boss Eddie Howe said the club would review the official match DVD before deciding whether to ask the league to credit the goal to Pitman and chalk it from Feeney's tally.
Pitman told the Echo: Feeno struck it well and it definitely hit me before it went in. Like any striker would, I am claiming it. The ref also said it was my goal.
I don't think it matters who scores at this stage of the season because the most important thing is to win. It's nice to get to 20 league goals but milestones have never really bothered me.
Hayter, who claimed the Cherries golden boot for five successive seasons, notched 20 league goals in 2005-06, while Clarke hit 26 in 1985-86.
Since Ted MacDougall plundered 42 in 1970-71 and 35 the following season, no other striker has reached the magical 20-mark, although Luther Blissett, Jimmy Quinn, Steve Jones and Jermain Defoe all went close.
Feeney joked: Brett's got plenty of goals so it's about time he started sharing them around he can definitely have the second one!
We're both trying to claim the first one. I didn't see him touch it so, as far as I'm concerned, it was my goal.
We will have to see who they give it to. It doesn't really matter who gets the goals as long as we win.
If I can have it, I will take it.
Victory saw Cherries reclaim a place in the top three after a number of their promotion rivals came unstuck with Rotherham, Bury and Chesterfield all losing.