I suspect what your interlocutor had in mind was in fact using a git rebase instead of a merge.  Consider the following simple diagram which will demonstrate what a rebase is.
master: ... A -- B -- D
local:  ... A -- B -- C
The above diagram attempts to represent the state of the branches when P1 attempted to push his work.  Both his local branch and the remote master are identical up until commit B.  But P2 has pushed commit D on top of master, and then P1 made commit C locally.  If P1 were to pull the remote master, merge, and then push, we would have the following diagram:
master: ... A -- B -- D -- M'
local:  ... A -- B -- C -- M
Now we see that both the local and remote master branches have merge commits (labelled as M and M').  However, there is an alternative here.  P1 could have rebased his local branch on the remote master branch, via this:
git checkout local
# do a fetch if not up to date already
# git fetch origin
git rebase origin/master
Now here is what the diagram would look like after rebasing:
master: ... A -- B -- D
local:  ... A -- B -- D -- C'     (C' labelled as such because it is a new commit)
Pay attention here, because what rebasing has done is to rollback the local branch to the most recent common commit between itself and master, which is commit B.  Then, it replays the commits from master, which in this case is just commit D.  Finally, it applies the commits which were unique to the local branch, in this case commit C.
The nice thing about this, which you can hopefully see, is that P1 can now just do a normal git push to bring his commit into the remote master:
git push origin master
This would leave the diagram looking like this:
master: ... A -- B -- D -- C'
local:  ... A -- B -- D -- C'
Now there is no merge commit on the remote master branch.
Note that rebasing usually involves rewriting the history a branch, and this can have complications if the branch being rewritten has already been shared publicly.  In the case of P2, if his local branch is being used only by him, then there is no penalty for rebasing it.  The remote master branch was not rewritten by the exercise we did above.  But this may not always be the case, and is something to keep in mind.