When you buy a Reit, you are not a fractional owner of a string of properties. You will be another anonymous shareholder in a company that happens to be dealing with properties and returning you dividends. This is much like any other companies out there who is dealing with any other form of business(e.g, selling newspaper) and returning dividends to you.
Reits are leveraged instrument. True. So are any other companies that employed leverage(debt). It is just a matter of amount of leverage employed. But it is not the same as you leveraging your CAPITAL in your investment. You will not get the full effect of the leverage. For example, if a company by virtue of its leveraged gained 20%, the value of the company might be up by 20%. The share price might reflect the revaluation and your INVESTED CAPITAL in it will go up by 20%. Reits behaves like any other companies with leveraged out there in the stock market.
However, if you leveraged on your investment in Reits, you will pay $20 and borrow $80 to buy $100 worth of shares in the Reit. If the same Reit have a re-evaluation gain of 20% and the share price goes up 20%, you will have essentially gotten back 100% of your INVESTED CAPITAL.
In conclusion, Reits are leveraged instrument(like other listed companies with debt) ,but it is not equivalent to a leveraged investment on your capital and you do not gain fractional ownership to properties. You are just buying a company listed in the stock market that happens to employ leveraged(like most of them) and paying you dividends(like most others) with gains that are not leveraged.
By the way, I do not recommend leveraging on your capital to buy shares. Read
Createwealth8888's Understanding Debt, Risk and Leverage on the danger and risk of leverage. Though, I would think if leverage on investment is needed, the only one I would do will be properties.