In general, syndicators use a combination of both debt ("traditional financing) and equity (the syndication piece).
On the debt side, they would source say 70-80% LTV (from Fannie, Freddy, a bank etc...)
and they would have an interest rate in the 4-4.75% range.
On the equity side, they would source 70-90% of the needed equity (from private investors, private equity etc...) and provide the additional 10-30% from their own capital.
In exchange, they usually give the the investor 70-80% of the cashflow and upside, usually yielding the investor 12-20% on their money. The reason that the investors require these higher returns is because they hold a much riskier position than the bank, as if the property value falls by say 10%, the investors lose half their money.
In the same situation where the property value falls by 10%, the bank still has their position covered by the property value and they don't lose anything. So as you can see from this example, the bank is in a less riskier position and thus does not require as high of a rather of return. The reason the banks aren't interested in lending at a higher LTV is because they are in the business of lending on collateral, not in real estate investing.
So to answer your question,syndicators use debt as that is they're cheapest option. However, since the banks would not lend then them full amount, they are forced to use a different sources (private investors etc... who require the higher rates) for the amount above what the bank would lend.