The original post is from 2014 - at that time it was not a popular problem.
Today it is different and happens way more often.
I dont know how OP worked aound it ... I nowadays have 3 quite obscure procedures that make sense.
Nasty thing with this particular problem : typically everybody will consider this issue as something hardware related.
So VMware support usually gets away with showing you some vmkernel-logs. So the support-case you may have opened gets relabelled as "Recovery-case and per definition VMware supports can run away again and so once the problem "flat.vmdks becomes unreadable with I/O error" can be blamed to an undefined hardware issue - the chance that the enduser gets help with the recovery goes down the drain.
My personal statistic for what I call the ESXi-Diva-mode problem is not95% hardware - 5% ESXi-VMFS-problem but more like 60% ESXi-VMFS-issue and only 40% hw related.
Anyway - all cases that I managed to resolve in the last few weeks were done by using a Linux-LiveCD-VM and carefully avoiding everything that could make ESXi think that a normal host from the cluster tries to read the files with I/O errors.
When possible read the files with the I/O-errors not from /vmfs/volumes but rather from Linux in ro only mode in /mnt/esxi/dev/disks/<device>.
Instead of copying a flat.vmdk I recommend to copy a set of pieces you specify as a long list with dd-commands.
When that also fails use a vmfs-fuse build - but not the outdated one from Ubuntu and other repositories.
Sorry - I see that this does not really help you - but at the moment I am not aware of a straightforward procudure that works in the majority of cases.
When I found one I will write instructions ....
Questions - see my signature
Ulli