I think warranty work is done at a preset dollar amount per task, reimbursible to the dealer from Triumph NA. Also heard it's a lowball amount and is incentive for the dealer to push off warranty work since it doesn't pay, or to tell you it's not covered so you'll pay.
I would suggest you document everything! This includes notes, who you talk to, what is said, dates and times. Put your complaints in writing and keep a copy for yourself. Be sure to obtain a copy of any Warranty Repair Order or Work Order. Demand a copy if necessary and if the dealer will not give you one, be sure to document that fact. When you pick up your bike, get an invoice. The dealer may claim that you are not entitled to an invoice because there were no charges (you were not invoiced for any repairs). You should be able to get a copy of something that says what the problem was, who confirmed it, who said it wasn't warranty work, the estimate for costs since warranty was denied (and you should have to OK anything that you'd have to pay for), and that you turned down the work. It is up to you to prove repair attempts if it comes down to legal action. The final invoice shows what was or was not repaired.
Make absolutely sure the dealer records your complaint on the work order exactly as you describe it. In 500 miles, just about anything should be covered by warranty and tell the dealer that. If they insist that Triumph corporate told them it was not covered, tell them you plan on writing a letter to your state attorney generals' office, and then do just that, and send copies to Triumph corporate, and the dealer. It may do no good, but at least you'll be on record where it counts.