Some of the arguments the conspiracy theorists use are quite hysterically ludicrous. The main one that seems to crop up over and over again is that the western immigrants (Sussex, Hampshire etc) can't be natural due to the distance across the channel unlike the Kent ones, suggesting that once they hit the north coast of France they start using road maps to locate the shortest route

. As best as i can tell this seems to stem from birders who are perhaps mistakingly comparing butterfly (and by default insect) migration to bird migration. Broadly similar yes, but birds live long enough to learn the route that has the shortest sea crossing and over time these become the main migration routes. Every single LTB that has ever migrated is several generations removed from the last one that made the crossing so there's no mechanism for this to evolve, certainly in the short time that LTB have been coming to the UK in numbers.
The other one is that they turn up in the same places every year

. Well of course they do, it's a known hilltopping species, and a hill that also has plenty of foodplant is going to be a magnet for both sexes. And off course once its known to photographers then they'll turn up every year too, ignoring a nearby hill that might also have some every year. Clouded Yellows seem to turn up in the same places year after year too but I don't see the same arguments for their 'miraculous' appearance.
I'm sure there are a few deliberately released individuals every year but with so much empirical evidence available, for those to cast doubt on all the others is it bit like me rearing a few Small White's and then assuming all the Small Whites in the area are mine. In fact far more likely to come across a captive reared Painted Lady in the UK that a LTB.
The main culprits are now so invested in their own opinions being fact, having touted them for several years, that no amount of genuine evidence is ever likely to change their minds.