Old English is a slightly fictitious language. There were several ethnic groups in Britain after the Romans left, and several distinct languages, hybrids and creoles. There was almost certainly, along with the many dialects of both P- and Q-Celtic languages and hybrids thereof spoken by the majority serfs, a lot of Frisian, Dutch and Flemish, as well as Saxon, Norse and other languages we can only guess at. The languages with the greater numbers of speakers were not those of the literate influential numerically few elite so their part in making modern English has not been recorded. Since they shared common ancestors or at least derived substantial parts of their vocabulary from a common pool, or group of pools, the finding of substantial similarities between a selected few of all the linguistically diverse texts of Pre-Norman England and a few Frisian texts of about the same period does not prove that Old Frisian is the closest relative of 'Old English'. It only indicates that there were some literate people using a form of Old Frisian in England at the time - that is assuming the texts weren't imported from the continent.
The languages and dialects now being called Old English are only a very few of the languages and dialects which contributed to Modern English. Most of the makers of modern English were illiterate. There's a grave danger of taking out of context the texts from which language historians theorise about the origins of English and according them disproportionate importance.
Vyvyan Ogma Wyverne