It depends on the period you're looking at. When we talk about 'history being written by the winners' what we are generally actually discussing is memory - not what happened or what we can show evidence for, but what the general public thinks happened. There are many examples of skewed public memory of historical events - the Lost Cause, the 'Lions led by Donkeys' myth of the British Army in WWI, the idea that the Treaty of Versailles crippled Germany and caused the conditions for the rise of the Nazis, the idea that the Nazis won the 1933 election, etc. At least three of those examples - the Lost Cause and the Germany ones - are actually a case of the loser in a war managing to define the cultural memory, or at least of that memory siding somewhat with the loser. Each community that experiences a particular event will have its own memory of that event, and those memories will be built upon, mythologised and politicised in a myriad different ways regardless of whether or not any of them are true.

However, within history itself, there are issues that arise. In general, the issue is not that History is written by the winners. The issue is that History is written. Historians generally consult written evidence first, and other kinds of evidence second. This means that our view of the past is highly privileged towards the documents (and other kinds of evidence) that survived and that we have access to. For example, we know very little about the practices of Druidic religion in Ancient Gaul and Britain - and what we do know we know because it was recorded by the Romans. Therefore our picture of that cult is defined by the things its enemies wrote about it, no matter whether we believe or disbelieve those things.

Further, historians inevitably colour our interpretation of whatever sources do exist with our own cultural biases, and our choices of what to study are not necessarily neutral - historians who grew up and lived in Imperial Britain, for example, tended to favour a narrative of Roman expansion and conquest which removed the moral onus of aggressive war from Rome and put it on the peoples Rome conquered and subjugated - the so-called 'defensive imperialism' hypothesis. Similarly, enlightenment historians chose a narrative of decline and fall for Rome that ended with the collapse of Imperial power in the west - conveniently allowing them to ignore what they called the 'Byzantine Empire' that survived in the east, because that empire, with its theological disputes and articulation of a divine right of Emperors, held too many parallels with the contemporary ancien régime states those historians opposed.

History isn't written by the 'winners' (whatever that means - how do we define a 'winner'?) - it's made both by historians and by public memory. Both of those things can produce false narratives.