It's literally true. A publicly traded REIT is a stock, so the minimum is one share, and with brokerages that offer fractional shares it can be less than that. Share prices for listed REITs commonly sit somewhere between about 15 and 150 dollars. No license, no accreditation, no special account. A normal taxable brokerage account or an IRA both work, and most brokerages charge zero commission on US-listed stock trades now, though you should check your own broker's schedule since it's their choice, not a rule.
On fees: if you buy an individual REIT, there's no fee layer between you and the company. The management team is paid out of the company's own expenses, which shows up in the numbers you're already looking at. If you buy a REIT index fund or ETF instead, you pay an expense ratio, and broad REIT index funds tend to run somewhere in the range of roughly 0.07 to 0.5 percent a year depending on the fund. That's the number to compare, and it's disclosed in the fund's own documents.
The fee that will bite you is the one you brought up sideways. Non-traded REITs, which are sold privately rather than on an exchange, often carry much higher costs and sales charges and you can't sell them whenever you like. Those are a different product wearing the same name. If it doesn't have a ticker you can look up and trade during market hours, it isn't the thing being described in this room.
Since you mentioned income: REIT dividends are mostly taxed as ordinary income rather than at the lower qualified-dividend rate, which is why a lot of people hold them inside a retirement account. Confirm your own situation with a tax professional.