It doesn't matter a toss if you can't see any difference between a tent and a bivvy. It may not even matter a toss if there is no appreciable difference between a tent and a bivvy. Whilst it might come down to nothing more than semantics, or simply what the manufacturer described the thing as, the fact remains that there are legitimate reasons for tents, but not bivvies, being banned on some waters. Some places are subject to planning restrictions that do not allow camping or tents, yet do allow long stay fishing from a bivvy. The fact that you might struggle to tell the difference is immaterial. Similar dubious caveats exist in many fishery leases. Landowners seemingly having no issue with bivvies and long stay angling, but specifying no tents and no camping.
Railing against such things, even if they do seem elitist and unfair, probably won't get you very far. Moaning about jobsworth bailiffs may also be a little unfair. Yes, some can be overly officious, but they may just be safeguarding the long term future of a fishery. The tent you are using, even if it is olive green, and as ridiculous as it may seem, might be an effective breach of planning or lease conditions.