You have no idea why Parker wasn't there so no need to judge and make assumptions. There are plenty of valid reasons why he couldn't have gone. Also, meeting with the President (any President) doesn't mean anything. The new president has yet to demonstrate that he is more than just talk. You can ask the tech industry leaders how useful and worthy their meeting with Trump was especially in view of his immigration executive orders - most of them signed petitions against it. In the end, Congress is the ultimate decision maker in this country, not the President, and maybe there are enough lobbying groups to push the industry's interests in front of Congress.
1. Why not take Parker at his word? The big company meeting was more important to him. But, he could have attended the White House meeting and still have made it to his company meeting by early afternoon. By not attending the White House meeting (unless cleared to miss it by Pres. Trump), he definitely risks offending a very thin-skinned person, with possible later detriment to his company.
2. While it should be true that the Congress is the ultimate decision maker, it is not true in practice. Congress has abdicated responsibilities to the Executive and to agency rule-makers. The President has tremendous influence that can be brought to bear, for ill or for good, affecting the airline industry.
3. You are probably correct that these White House meetings have little in the way of immediate importance. But first impressions are important, and if Mr. Trump takes a liking to you early on you are more apt to get favorable treatment down the road.
4. Lobbyists pushing Congress is, of course, one of the reasons Mr. Trump is in the White House. If you are pinning your hopes on lobbyists, don't look for the situation to be improved. Lobbyists, money and Congress, taken together, are a terrible affliction on this country.
Facts are fragile things. Treat them with care. Sources are important. Alternative facts do not exist.