Is it true that the 100 most common English words are all Germanic in origin?

is there any accepted/standard list of the 100 most common English words?

I suppose it all depends on your definition of authoritative, but I think a good start is The Oxford English Corpus, a collection containing over 2 billion words of 21st century English from around the world. Here's a list of facts about the corpus, including the 100 commonest words in the English language.

Neat facts about distribution: 10 lemmas (word forms, is and are are lemmas of to be) make up 25% of the corpus, 100 make up 50%, 1000 make up 75%, 7000 make up 90%, 50,000 comprise 95% and you need over a million to get 99% coverage.

So, one quarter of all words used are the, be, to, of, and, a, in, that, have, and I.

Is it a myth that they're all Germanic in origin (as I now doubt)?

Yeah, most of them are germanic in origin, but not all.

As you noted:

use is of Latin origin (by way of French) and replaced the O.E. verb brucan (which survives as the verb brook "to tolerate, put up with something unpleasant")

because is of direct Latin origin from the phrase bi cause "with cause."

and

people also Latin by way of French.

Those are the only words that jumped out at me. Of course, most of the common words have Indo-European origin, so they'll ultimately share a common root anyway. See two and duo.

It's usually pretty simple to spot Latin loans, even if they were borrowed in the common Germanic period. Grimm's law means that most of the consonants are different in inherited words and Latin loans.

Also, it's worth noting that English also has a certain amount of words borrowed from Norman as well. Which means that in some cases you have three versions of what is essentially a single proto word: an inherited version, a Latin loan, and a Norman loan. The last two will of course be quite similar, but not identical.

As to your question, I'd be surprised if there are no loans at all in the top 100 words. If nothing else, some of the personal pronouns ("they" and "them" if memory serves) are borrowed from Norse. A related language, yes, but inherited forms would be different from what we have in modern English.

Here is one site that blends British, American, and Australian English together: http://www.world-english.org/english500.htm

In general, the Germanic words adopted into English mostly have one or two syllables. While this also describes some words with French or Latin origins, most of the multi-syllable words in English come from these sources, rather than German.

But the easier, Germanic words, make up most (not all) of the "top 100."