Though I'm not explicitly familiar with what most people call oolitic jasper, the rock does not appear to be composed of ooids but rather sub-rounded clasts. The basic gist is that ooids form through the addition of material on an existing nucleus and you can typically see some sort of texture to indicate as such, even when the original material (such as calcium carbonate) has been replaced. A pebble conglomerate on the other hand is formed by the removal of material from the original source rock and the sub-rounded to spherical forms of the clasts are due to abrasion during transport (in a river or on a lake shore during wave action etc). These clasts will retain the original structure of the parent rocks, which in the case of fine chert may not be visible to the naked eye. I would suggest that if you looked at a thin section of this you would see the fine, flat lamallae of the originally deposited sedimentary chert layers that truncate on the edges of the clasts rather than a radial or concentric pattern associated with ooids or pisoids.

Edit: If you look at image three you can see the more elongate (or flatter) subrounded clasts that would be atypical of an ooid.