Yes it does mean rock. Petros means a small rock or stone. On the other hand, petra, which Christ said the ekklesia would be built on is an unmovable rock.
4073 (pétra) is a "solid or native rock, rising up through the earth" (Souter) – a huge mass of rock (a boulder), such as a projecting cliff. [http://biblehub.com/greek/4073.htm]
4074 (Pétros) which is "a detached stone or boulder" [http://biblehub.com/greek/4073.htm]
So I agree with you. Someone's interpretation is wrong. Peter indeed was call a "detached stone or boulder". Something movable. But Jesus said He would build His ekklesia on an unmovable "huge mass of rock". Would you rather be part of an ekklesia build on a moveable "detached stone" or an unmovable "huge mass of rock"? I think the Holy Spirit chose the words He used for a reason.
I believe the rock Jesus is talking about is Peters faith.
I tend to agree with you but I believe Peter is not to be taken lightly in view of the other things Jesus said.
19 And I will give unto thee the keys of the kingdom of heaven: and whatsoever thou shalt bind on earth shall be bound in heaven: and whatsoever thou shalt loose on earth shall be loosed in heaven.