Dude is trying to sell you services and doesn't know one of the ways that Vanguard is special. In dude's defense, Vanguard's own materials, while not putting numbers on it, seem to agree with him that ETF's are more tax efficient than funds. But the specific funds in question VTSAX and VTI show a different story.
Vanguard has a proprietary structure to its funds which allows VTSAX to have the same tax consequences as VTI - namely there generally aren't any capital gains distributions from the fund. They have a class structure where ETF's are a class of shares in the same fund as the regular mutual fund. They did that so that the mechanism by which ETF's reduce capital gains taxes for investors can benefit the mutual fund shareholder's too. You can see from the link below, nothing except for dividend distributions for a long, long time. Realized gains negative.
https://investor.vanguard.com/mutual-funds/profile/distributions/vtsaxCompared to Schwab's distributions which include dividends (listed as income) and long and short-term capital gains.
https://www.schwabfunds.com/public/csim/home/products/mutual_funds/distributions.html?symbol=SWTSXVTI and VTSAX hold the exact same portfolio. The dividend distributions will be the same. The capital gains distributions are also the same - namely zero. How exactly are you saving taxes by holding VTI vs. VTSAX?
Finally I'll note that ETFs have additional costs you may not have thought to look at - there is the bid-ask spread, which is pretty low at .01% for VTI. But even if it is real, you just paid that much up-front since you bought at the ask price. You'll pay it again when you sell at the bid price - any time you transact. There is also the premium / discount - as of right now they're quoting a $0.01 / share premium (rounds to .01%). So if you bought at that exact price, you paid a penny more than NAV for the shares. That can work either way, and for a liquid ETF such as VTI is minimal, but it is a potential additional cost on both buying and selling as well.
So basically, the differences in cost between VTI and VTSAX are minimal, and could favor either option depending on exactly where the market is when you transact. I'm using VTSAX because it is more convenient for me. I put the money in, I get NAV pricing at the end of the day. Very simple.
If you really want to be able to buy or sell throughout the day, or place limit orders or whatever, then VTI is obviously a better choice. Cost is a much less compelling choice in this case.