Quite simply because we have available a written document saying that it happened in 1066 and there's no reason to distrust this simple date.

While historical sources are of course always subject to scrutiny and suspicion, by the time of the battle of Hastings, most of western Europe was on the same page when it came to calendars and dating. At the same time, written sources are not evenly scarce. Court documents, hagiographies, and church records are often quite well represented even in normally not well attested time periods. England in 1066 was actually quite ably administrated and there are extensive documents, literary, secular, clerical, and so on all available from this time.

In the case of England specifically we are blessed (and sometimes cursed) by the existence of the Anglo-Saxon Chronicle which recounts the year to year events going on in England, from Roman times up until the 12 century. Now of course there is a tremendous amount of information in these sources that is just not reliable. The sources are also not unbiased in any way, and are a later composition.

However despite all of these caveats it seems a little overly hostile to attack the record of significant battles that were recorded nearly contemporaneously. The Chronicle was still being updated, or rather one version of it was, well after the Norman conquest.