Document in "Read-only" mode all the time

Another person with this, or certainly a similar problem (I'm working with a document that I've opened via the Browser, not the OneDrive sync client). I'm working on a customer site (using their wifi to connect to their SP Online tenant from my laptop that I've logged into using my organisational account)

Scenario is where I've worked on some documents in my OneDrive and when completed the first draft I've uploaded these Word documents to a SharePoint library on my customers tenant where they have reviewed. 

They've provided feedback and I now need to update the document. I can only edit the document in Word Online. 

Each time I click the "edit in word" button , the document will open in the Word client but only ever as (Read Only).

I can save as and overwrite the server copy but the document in Word still is a (Read-only) document.

My collaborator on the Customer side has closed out of the document and has repeated the same steps as I on his machine. The document opens up on his machine , in Word , for editing. 

I'll have to continue to use Word Online. which is not idea as I want to copy and paste in some screenshots into the document , and Word Online is not allowing me to do this! - advising me that i can only upload image files stored on my machine and not copy and paste :( 

I've heard other people complaining about this issue before.. Any ideas what the solution is or why it's happening? It's hardly "by design" is it?