Being told that voting "no" was the only way to retain EU membership was one of the sticks that the Better Together/No Thanks side consistently used during the indyref campaign, along with other myths such as not being able to use the pound as currency.
Indeed, if Scotland had voted to become independent there was no concrete guarantee that it would have been able to join the EU immediately and we'd have to go through the formal process, but considering that we're fairly well aligned (or were) as part of the UK, it wouldn't have been a massive hurdle to overcome.
I agree that it was debatable whether or not Scotland would have just been allowed to carry on as an EU member. The UK wouldn't have objected, only the Spanish might have felt it necessary to block. To that end, voting for independence would have been a better bet even for continuous EU membership, let alone the only way to guarantee future choice.
I'm afraid if you feel people lied to get you to vote one way or another, you'd have to take that up with them. The country can't upend itself because some claim they believed these things and therefore voted to stay. These aren't subtle ambiguities, but things which people really ought to have been able to work out for themselves.
Same with the other thing you quote, about the Pound. No there was nothing to stop an independent Scotland creating its own Pound, or even using the UK Pound in the same way as some non EU/US countries use the Euro or the Dollar. But in the former there was no guarantee of parity with the UK Pound, and definitely no underwriting from the UK treasury without UK consent (aka monetary union, which wouldn't be in the UKs interests, being as it would then act as guarantor for Scotland's economy as today minus any semblance of oversight and governance). In the latter you've got no control over fiscal policy and effectively no central bank. You'd have to use the Pound and just hope that UK monetary policy worked out Ok for you - hardly "independence" (although funnily enough that's what Scotland would get in joining the Euro...). There was no other option than those two. Anyone who suggested the UK would be compelled to share its currency and underwriting with a third country doesn't understand that "independence" is something which goes two ways.
As I say, the UK was due an EU referendum and it was openly stated a vote to remain in the UK could result in leaving the EU. I don't see how that could have been misread no matter what anyone said.