I chose my words carefully: you are owning the same fraction of every company in a cap-weighted index. If every company in a cap weighted fund has a billion shares, Then the fund would own, say 10,000 shares of each company in the index.

Yes, in that sense.

However, a minor point: there are no "cap weighted" indexes in that sense. (and QQQ isn't even close). They are almost all "float adjusted". So you're not getting the same fraction of each company, you're getting the same fraction of the listed and tradeable portion of each company. Some indexes will exclude various types of restricted or insider shares or shares held by other companies (often parent companies) or governments.

I guess a bigger question is simply questioning why you would want to own the same fraction of each company. Bigger isn't (statistically speaking) better, so why buy more of the big ones? The reason cap weight index exists is because it's easy for a fund to track, not because it's what's best for investors: until an index change or M&A, no trades to do, but riding confidently into every bubble.

Jim