I know nothing about them DRs, however I want to buy one and take it to Mexico so I absorb the info on them.
Fuel filters, looks like there are 2 of them, one at the petcock and one at the carb.
I am surprised the "tech" didn't try to spray gasoline in the carb as he tried to start it. If that gets the bike going, even temporarily, certainly would point to a fuel supply problem.
Another thing you could try if you suspect ignition problems is to try starting the bike in the dark just to make sure the spark isn't jumping somewhere. That happened to my little XR.Easy diagnostic once I tried that.....not so in daylight. You can at the same time spray water at the plug wires/coil, if either is cracked you may see the spark jump.
You could also remove the spark plug wires, if they are removeable as I think, and do an Ohm test on them. If they are carbon wires you may want to twist/bend them with the meter connected. My bike was giving me weird readings doing that, continuity then not.....damaged inner carbon core.