... as miners may announce false support for a fork, and stay on the standard bitcoin chain when it is time to switch. A variant of this happened after the BIP66 soft fork, which was triggered on a 95% majority, resulting in a long chainfork which took hours to resolve.
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The only variant was the SPV miners forgot to check the header properly and fucked up.
They didn't check the version number.
Not only the header; they didn't check the validity of the block at all. They announced support for the new consensus rules, without actually supporting them by checking if blocks were valid or not. I.e. a variant of false support announcement.
I made no argument against 95%, btw. However 95% of the last 1000 blocks will be triggered by less than 95% (see explanation by Organofcorti). 95% of one difficulty period (2016 blocks, fixed measurement points) is much more likely to be a certain 95%. At 95% of the last 1000 this somewhat premature activation doesn't carry a high risk of a prolonged fork, so it probably doesn't matter as long as there is a cut-off date where the soft fork will fail if not achieved.