I've stayed out of this for some time but.....
The bottom line is, You are either BOW HUNTING or you are BEAR HUNTING!!!!! Simple as that.
There is a "early" Bear Season with which you can use firearms. It DOES overlap the Archery Season by a few days,HOWEVER... The Archery Season is for Deer AND Bear!!! If You want to hunt Bear with a firearm,that's fine... HOWEVER, If you are BOWHUNTING with a firearm in your possesion,you are in direct violation of the law!!!
There is no "glitch" Your ECO is wrong!!! Also, IMHO he wouldn't be the first "dumb" Conservation Officer that I have come acrossed. More than a few of them don't know the laws they are supposed to enforce. You could take his line of thinking in other directions too... Squirrel Season is also open,but you can't carry a .22 then again,Turkey Season is also open... But,you can't carry a shotgun...
Plain said and done... Once the Archery Season starts,you better not have a firearm in your possesion if you are BOWHUNTING!!!
It doesn't get any simpler than that.....
(Thank You for listening, I'll get off my soap box now)