Bribing an expert is, in general, not illegal.
This seems to be an important principle, so it will be stated twice for emphasis: Bribing an expert is, in general, not illegal. It’s illegal to bribe public servants and union representatives, and under some circumstances it’s illegal to bribe a corporate employee (without the employer’s consent). But there’s no law against giving doctors, lawyers, scientists, engineers, etc. large sums of money in exchange for their support of you, your company or your product.
The public in general seems to place a nontrivial amount of confidence in experts of various sorts: expert witnesses at trials, expert professionals on commercials, expert guests on TV shows. But it is, not only commonplace, but standard procedure for all of these people to have their pockets lined in exchange for supporting a certain point of view. Even on an international scale, the only thing preventing ExxonMobil from just writing checks to all the world’s climatologists is the large fraction of scientists who really do value ethics over money, and the obvious negative PR that would result.