From what I could find, it doesn't look like these types of boxes are listed for any type of fixture support.
When looking at a box that attaches to a stud/joist using nails (B520P), it states.
Suitable for fixture support up to 50 lbs.
With the the old work version(B618R), it states.
Not listed for fixture support in ceilings.
A box like this (BH614R), states.
Listed for wall fixture support up to 10 lbs.
The last page of this catalog shows some round boxes, and the weight they are rated to hold.
Based on this information, I would say the box you want to use will support less than 10 lbs.
The best options in your situation, would be to move the fixture location to allow you to fasten the box to a structural member, or add a structural member to mount the box to.
Update:
I contacted a company that manufactures these, and here is their response.
[Link to product omitted]
As shown on the link above this item is not listed for fixture support. We do have several other boxes that are rated for fixture support.
[Link to other product omitted]
The link for boxes rated for fixture support, pointed to boxes that attached to structural members.
The instructions for the fixture are only correct for a metal box. If a metal box was used, the box itself would (should) be grounded. The bracket that holds the light would then be connected to the box, which would make the bracket grounded. Finally the ground wire from the fixture would attach to the bracket, grounding the fixture.
In the case of a plastic box, the box is not grounded. All ground connections must be made by connecting the ground wires together. So in your situation you are correct, you'll connect the ground from the supply to the ground from the fixture using a twist-on connector (or other approved connection).
Best Answer
It looks like that electrical box has a mud ring installed on it. The box itself is clearly of a molded type construction such as a phenolic or bakelite or plastic material. If the mud ring is made of metal it is possible that the original installer wrapped that ground wire around the mud plate mounting screw in order to ground the ring. This could be the reason that you cannot pull the end of the wire free.
It is unlikely that the ground wire exits the box completely and travels off to some other destination. If that is the case you may be able to reach inside the box and cut the wire in a manner to maximize its length and then simply attach the light fixture ground to the end of that wire.
An alternative, while not optimum would be to bend the ground wire back on itself so that it comes to a double width point. Then use a green wire nut to attach a bare solid copper wire pigtail. Then the pigtail becomes available for connecting to the light fixture ground.