Since RSUs generally require no "out of pocket" costs from you in order to acquire the shares and since brokers, even if basis is being reported to the IRS, only report the "out of pocket" costs - $0 - I'm somewhat surprised that you're seeing any number there at all. However, brokers do usually tell you the correct basis to use for these sales in some "Supplemental Information" that's sent with the 1099-B.
What sales category is the broker telling you to use for the sales? If the sales category ISN'T being reported to the IRS then the broker might indeed show the correct basis in Box 1E.
The RSU "Guide me" interview certainly CAN come to the correct basis, but many people find that interview somewhat confusing and I know that mistakes are made all the time. I'd expect that the broker does have the correct basis in this case and, everything else being equal, I'd go with the broker's numbers. But the correct basis to use here just isn't all that mysterious or difficult to figure out and, really, you should be able to determine that. For any given lot of stock acquired via an RSU the per share basis is the SAME AS the per share "fair market value" used by the employer to calculate the compensation created by the RSUs vesting and I'll bet that information was passed on to you at the time.
A reasonable approximation of that "fair market value", (assuming the stock is publicly traded), would be to use the stock's closing price at the vesting date. If you know the "lot" information that comprises each sale you should be able to work out fairly closely if TurboTax or the broker has the "right" number.