One answer above says that ti frames are “renowned for failure”. This is completely incorrect as a general statement. However, the welding does need to be done under inert gas so as not to let contaminants into the weld (I think oxygen is one of the potential contaminants). The crack above seems to involve the weld at the head tube, so it seems like some sort of contamination was involved.
As a general rule, custom bicycles will select tubing appropriate to the rider’s weight. For a heavier rider, a builder will unsurprisingly use stouter tubes. So, as a rule, ti should be suitable for a heavier rider, but any material can be made suitable.
I doubt that Enigma would have offered a refund. They should have offered to repair or replace the frame at their expense. Now, if you are not confident in the manufacturer, you could sell the frame, which would not be a very satisfactory solution - you won’t get the MSRP back on a new frame, and you’ll get even less on a repaired one. It is possible, in principle, to repair a frame. Ti Cycles in the US offers this as a service. Other titanium builders may if you aren’t able to get satisfaction from the original manufacturer, or you’re unwilling to accept their repair. However, I don’t know that all ti builders offer this service.
Under what circumstances should a rider not get the bike repaired at all? I recall a post on a different forum about a failed Enigma within the last 2-3 years, so I don’t think it was this rider. If you become aware of a spate of failed frames from a builder, then it might be better to just cut your losses entirely. This type of failure is an issue that, as far as I know, the industry discovered early on and has generally learned to avoid. If a builder has a number of weld failures, that means there’s a quality problem that they haven’t been able or willing to correct. However, two failures is not a spate of failures. Reports can be hard to come by, and any forum posts are likely to be slanted towards the most dissatisfied parties. So it’s hard to come by actual good data. Basically, I can envision a circumstance where I wouldn’t trust the original manufacturer’s work, but it would take a lot to hit that bar. Enigma is unlikely to have hit it.
In the absolute worst case if you give up on the frame entirely, I encourage riders to try to recycle it, as discussed here.
As to the bike shop supplying you an interim bike: this is sometimes a courtesy in the automotive world, but it’s not generally done in the cycling world. Bikes don’t hold their value as well as cars, so if a bike store were to maintain a loaner fleet, it would depreciate in value rapidly. In contrast, I bought an ex-dealer car that was certified used with extremely low miles for near the MSRP. It’s not impossible that the store owner might do you a favor if they have the right size of something, but I would look to borrow something from a friend, or fix up the old bike, or explore a rental for the events of interest. I would lean on Enigma to get the bike replaced/repaired quickly, explaining that I had events to ride in and that I would be displeased at undue delays.