I may be able to look into the ownership later in the week.
If you could get a definitive answer that would be a big help . I got the impression they where asking if i worked at either end . Not just someone out for a bike ride and scoping for oil protestors .
Looking at the various planning applications, the matter is 'unclear'.
A planning applicant has (by law, not council fussiness) to declare their land ownership and/or serve notice on those who own the land (lets not get technical about tenancies, leases, long leases) when submitting a planning application. That consists of signed certificates and a location plan showing the boundary of the planning application (the red line) and any other land they own (a blue line).
In relatively recent times there have been Hazardous Material Storage applications. An early one (11_01792_HAZ) shows a wiggly yellow highlighter pen line encompassing the whole site, including Oil Sites Road and the railway so is clearly not an 'ownership' plan. A later one (13_05540_HAZ) shows detailed red lines which generally exclude the whole width of the former sidings, mainline railway, more sidings and Oil Sites Road. But it is badly drawn on the north side of the road, the ownership not following recognisable features (fencelines, roadlines etc) which ownership generally does. The most recent one (17_04511_HAZ) has the same detailed (but probably sloppily drafted) red line with the exclusion of the science park (bought by the university in 2014). Applications for the science park show that ownership including the car park north of the railway near to the roundabout at the eastern end of Oil Sites Road.
I also looked at the Vauxhall plant, just up the road in Ellesmere Port. There the main road past the factory (North Road) is public, apart from a short section (460m) where there are big red signs including 'this is a private way which members of the public are not entitled to use'. Both signs say 'westwards from this point', so one of them needs changing! The western one says 'no unlicensed vehicles beyond this point' on the reverse so it may be a simple workaround to allow internal shunting of vehicles from factory to storage yard which would otherwise be illegal on a proper public road.
A similar situation may exist on Oil Sites Road but without a Google Streetview I cannot tell - there are clearly barriers across all four road lanes at Argent Energy Gate 3.
The public right of way, referred to previously, used to continue from the end of Bridges Road, eastwards to Folly Bridge over the Rover Gowy then southwards to come out on the A5117 at Avanti Gas Ellesmere Port. Historically it meandered through the fields where the refinery now stands so must have been diverted to then show on the 1-inch maps viewable on the National Library of Scotland website. Presumably! it was officially closed at some point with it not showing on the online definitive map linked above.