No, that's not true, either (I support the 17th, btw, 100%. Politicians should not be choosing other politicians to represent the people). What you're confusing is that in the very early days, it was impressed upon Senators (elected by the legislature) that they were supposed to serve the will of the legislature. If they could not follow their instructions on how to vote (or if there was a change in the party/ideological makeup of the legislature after the election of said Senator), they would be expected to resign at once and allow the legislature to vote in someone else that could follow their will (with the Governor appointing someone in the interim).
This really didn't last very long, since when a person discovered they could serve out the entirety of their 6-year term and were not LEGALLY required to follow the wishes of a given state legislature, especially if there was a turnover, they'd just ride it out regardless. It's why the arguments of those wanting to overturn the 17th ring hollow. This and many other reasons were why the 17th was enacted in the first place (another big one was open bribery of legislators). Even before the 17th, some states were already allowing the people to vote directly, as they were tiring of the corruption and how out-of-touch the Senators had become.
Well said, brother. Best explanation I have heard of the 17th Amendment and ramifications.