It is not true. The presidential candidate chooses his running mate. The presidential candidate undoubtedly seeks advice from people in his inner circle, but ultimately he makes the decision.
That's simply not the case. The President and VP actually run separately, and it's theoretically possible for the President and VP to be elected from two separate parties.
Ronald Reagan never wanted George Bush to be his running mate. Bush was foisted on Reagan as part of a GOP compromise.
And you'll never convince me that John McCain had any interest in running with Sarah Palin in 2008.
The VP candidate is generally selected by party insiders. That's why they always tend to be career politicians who are mediocrities and losers, and whose main qualification is their ties to party leadership.
Last time, Trump relied too much on advisors.