eteb3
Don't apologise because you don't even sound dense! OpenStreetMap (OSM) is like an iceberg of technical difficulty: the further down you go, the more you realise there is. (I speak as someone who regards themselves as a novice, after several years; and also as useful to the project because it's so easy for novices to be useful).

'The map' is the database (db), unreadable by humans. If your router is using openstreetmap, it's the database that it's reading. 

Before you can use it, the db must  'rendered' : pushed through a machine that makes it useful to humans. Often that's by making a pretty paper-like map using image tiles, sometimes it's by giving you a routing interface.

The issue here may be (1) an error in the db (which you may hear called 'the map') or (2) an error in how the db is being rendered.

The visual presentation ('rendering') of your map in grey/white doesn't make it any less based on OSM. 

On this particular issue, I think Thingummy is investigating the effect of the barrier. He's moved it off the route, so maybe that has fixed it but the routing software is taking a while to update: see here https://wiki.openstreetmap.org/wiki/Routing#Checking_your_fix

A puzzle for me is that Graphopper and OSRM have no trouble: it may be worth raising a ticket with your routing app provider. It's a fact of volunteer projects that things will move rather slowly to a resolution: if you're paying them for their service, they may be paying someone to sort it out. Not least, it's not obvious that they are using OSM as their base 'map' (ie, db) - I just got a trial login at MyRoute app and on the desktop version, top right of the map pane you can select your 'layer', or rendering (trial version gives OSM, CycleOSM, and Michelin) - so it could be that the visual presentation is one of the in-house OSM renders (possibly OpenCycleMap from your description) but the routing itself is coming from different sources. 

That's all rather inconclusive, I realise. Sorry...