Yes, it is possible to pay capital gains tax while holding a mutual fund that has gone down in value.
Mutual funds have something called “capital gain distributions.” Inside a mutual fund, when a manager sells an asset for a gain, that gain (cash) has to be distributed among all the holders of the fund. This is paid out to everybody either in cash or by issuing additional fund shares, similar to how dividends are paid when you hold individual stocks.
When you receive these capital gain distributions, you need to pay capital gains tax on them.
I personally have been in this situation: The value of my mutual fund investment had gone down (due to a down stock market). However, because I had been given additional shares over the year from capital gains distributions, I had to pay some capital gains tax even though my investment had gone down in value and I hadn’t sold anything.
However, it is not accurate to say, as the article does, that in this situation you are paying tax on someone else’s gains. You only pay tax on capital gains distributions when you are actually given the distributions (proceeds from the assets sold at a gain), either in the form of cash or additional fund shares.