Thanks Mike! I called E*Trade the next day and they gave me a stupid answer:
Since this account of mine was automatically moved to Morgan Stanley after the merger of E*Trade and Morgan Stanley, its status is "closed" in E*Trade, and for some stupid reason, E*Trade only provides PDF version of 1099 forms for a closed account, without ability to export it to Turbotax.
Again, it's stupid, but anyways, we found out why.
