Why are rose suckers a problem?

A gardening friend viewed my garden this weekend and informed me my bush rose (not sure of the type) had a sucker that has erupted about 2ft from the rose and standing quite tall compared to the bush. Now this has some stunning roses on it, slightly different shade from the bush -- is it really a big problem? Can't I just keep the area well fertilised so they both thrive or should it be killed off :(
The rose bush is an older one that I salvaged after moving in - it's been uprooted and replanted several times, poor thing and got a very hard prune in the spring. We thought it was dead, but it picked up and is absolutely beautiful and healthy.

 

Sorry adding to my post - from reading the Internet I think she might have been wrong that his branch is a sucker as they shouldn't bloom? I haven't dug down to see where it's coming from, is it possible that a piece could have broken off underground and is now starting to grow on its own? Or maybe did I bury it too deep and a branch has managed to creep out by 2ft?

 

Thanks wiseoldowl, very helpful!

... I will investigate by the light of day when I get a chance.
The flower on my potential sucker is bright yellow - identical to the flowers on the bush itself ... It's just that the shoot is 2ft away from the bush!