Moreover, in what way would a full node be helpful here ? A full node would have stopped for good when the first false block was mined.
Wrong. The node will ignore the false block as if it had never existed.
Such is the power of nodes.
The problem is that you didn't even understand the logic of the arguments here.
Achow101 argued that a risk of using SPV is that one could be tricked in accepting a transaction that was present in the correct block chain that was at the same time a double spend. In order for that to be a risk, you have to accept already that there HAS BEEN a double spend somewhere in a past block that is included in the current block chain on which everyone is building. It means hence, that there was a past block (say, block number 506072) that contains a double spend, and that miners are still happily building on top of that. Otherwise, the SPV user cannot be tricked in believing such a double spend, because it is not present in the block chain. So one needs to reason as if that were the case.
Achow101's argument is that if such were the block chain, that my SPV client could be tricked in accepting that double spend as true. That is correct. My SPV client could indeed simply be convinced that, as it stands, a given transaction was indeed, in the actual block chain and I wouldn't know that it was a double spend that miners had simply accepted.
MY argument, like yours BTW, if you could think somewhat logically, is that if ever that were the case, then bitcoin is broken. It means that already for a week or so, there is an invalid block in the chain, and miners don't mind, exchanges don't mind, nobody minds.
Now, if ever that were true, that is, if miners did include a double spend in block 506072 and continued to mine on top of that, then every full node would come to a full stop at block 506071, because they would reject block 506072 as invalid (containing a double spend). However, as miners have been mining on top of that invalid block 506072 by hypothesis, and are now at block 507762 or so, there is, nowhere in this world, a successor prong to block 506071 that full nodes would accept. The only blocks that have been made are 506072,506073.... 507762 and are ALL INVALID according to the full node, and no other blocks have ever been made. So it comes to a full stop, for good. Because no "good blocks" 506072, 506073,... have ever been mined.
The difficulty with this kind of argument for a limited mind is that it contains too difficult a form of argument which is called "reductio ad absurdum". So it is quite normal for some not to be able to follow.
https://en.wikipedia.org/wiki/Reductio_ad_absurdumI claim that SPV is secure.
Achow101 argues that there is a case where it is insecure.
My argument is: if ever your argument were true, then.... (absurdities) ; which you confirm (!).
Hence, Achow101's argument cannot be valid, and hence my claim that SPV is secure, stands.