I don't oft post here, but my day job (ok, career) is such that I have some experience with this kind of thing. Warranty. Motorcycles.
First off, you've verified low compression and leak on #1 cylinder. Have you physically taken the bike to the dealer and asked them to perform a diagnosis? Most warranty statements require you to take failed machine to the dealer if you want any warranty work to be performed.
Secondly. "Normal wear & tear". I don't deal with Triumph but the other 4 brands that I DO deal with, yes, wear and tear is, in fact, a specific exclusion from warranty. That being said, there is no definition of "normal wear & tear", so that leaves the definition up to (1) the dealer and (2) the manufacturer. On my lines, if I have a question as to whether the manufacturer can/will assist a consumer with his equipment that is still within the warranty period, I call the manufacturer-or in the case of one mfg in particular, they have an electronic form that you fill out, with pictures, and send it into them for pre authorization. They don't require it but it's good practice to do it (as a dealer) BEFORE going too deep into a repair job. After all, it looks a LOT better from the customer's standpoint if dealer calls and says it'll be $300 to do teardown & inspection, and if warranty denies the repair based on what is found during said teardown & inspection, you'll be out that $300....but on the other hand, if they ok it, you don't owe a dime. That's called communication with the customer and is a priority-or should be anyway. So, what is Triumph calling normal wear & tear? Are they insinuating that these things normally wear out within 2 years' time? THAT is the question....since I don't have anything to do with Triumph.
Thirdly, If you're tearing into the engine already, warranty is not likely to help you. Repairs-if you expect any warranty to help, are generally to be done by an authorized dealer ONLY, and generally that also means that they're NOT going to just give you parts so you can fix it....they have to do 100% of the repair, for many reasons. Also, expanding on that, if you have any modifications that might increase the power level, they can deny based on that, too. People sometimes misunderstand the magnussen-moss act (I think that's what it's called)--which is designed to protect consumers, but if you read into the whole act, it doesn't specifically protect you from everything...so if you have, for instance, an H2 and run out & put a pipe on it, burn the engine down, then the manufacturer deems the engine failure to be caused by the aftermarket pipe, you're going to pound sand. Simply adding the aftermarket pipe doesn't void your warranty. The effects of the pipe, however, can be the source of a denial of claim, again based on what the effect caused-and trust me, they'll get the engineers involved along with doing coolant and oil scans, requesting service records, etc. Worth mentioning-especially with motorcycles since almost all of them get customized in some sort of way. Personally, if "they" (mfg) doesn't ask, I don't tell. But if they do, I can't/won't lie to them.
Now to the technical side. Doing a leakdown test is easy. Remove spark plug and have some way to keep the engine from turning. Turn engine to TDC compression stroke on the cylinder you're dealing with, in this case #1. Set your leakdown tester, then attach it to the hose that is in the plug hole. THe engine WILL want to turn over, so be ready for it. What's the gauge say? Is the engine cold or hot? Ideally you do a cold test, then add a small amount of oil to the cylinder through the plug hole, rotate the engine over a couple of revolutions by hand, then back to compression stroke TDC, then retest leakdown. If % comes way down, like from 20% to 5%, then it's piston or ring related. If no change or very little change, it's valve related. Easy. You'd want to see less than 10% leakage on a cold engine ideally. Hot, 5% or less. Be careful with the oil though and rotate the engine by hand only. Don't try to use the starter. I have seen connecting rods bend and break by guys using the starter to disperse the oil. Compression test is inconclusive on a lot of bikes because of the automatic decompression mechanism that many have. Sure you'll see 150 psi, but if you disable the auto-decompressor, it'll be 250+, so you see how it changes things. Most crotch rockets don't have ACR's and most cruisers do. Crotch rockets have typically have late intake valve closing point and consequently don't have a high cranking pressure which would negate a large starter, where a lot of cruisers-especially twins and singles-have "small" camshafts with an earlier intake valve closing point, which equals high cranking compression-and would need a BIG starter to keep from kicking back & destroying parts, so they put an ACR on them to avoid the huge starter. Do not know if Triumph uses an ACR or not. Now, if you have a cylinder leak, why? What is the actual cause of the leakage? Ring gap opened up? Broken ring(s)? melted piston? Worn cylinder? Then...if one of those, why? That's the questions that the manufacturer wants to know.
On the stuff I deal with, usually it's valve related....lack of maintenance..clearance closes up on the intake valves and then the valve is held open, engine still running, further wears the face and/or seat, more clearance, compression drops and eventually it won't even run on that lung. Quite common on anything that actually runs longer than 5000 miles. 88% of crotch rockets are total loss before 5000 miles....and yes that's a statistic....which is one reason insurance for all motorcycles costs so much.
Anyway...enough rambling...hope you can make heads or tails of it all.