If a fuel injector "stuck open" you would not get a misfire since the amount of fuel that could leak past is not enough to cause a big issue besides messing up the fuel trims real bad.That would set off codes P0172(bank 1) or P0175(bank 2) depending on which bank has the leaking injector,at the same time the PCM would be cutting fuel to that whole bank thus reducing the amount of leaking fuel even father(to a point).
Now if they had the key in the "run" position without the engine running for a extended period of time or did not disable the fuel system while doing the compression test they could have "hydro locked" the engine.Once that happens you have a very small chance(like 5% or less) that no internal engine damage was done if it happened while at cranking rpm's and not at driving rpm's(1000 rpm's+).
Being as your current codes are for 2 different cylinders on different banks either they caused the codes and did not clear from testing of you have more than 1 issue to deal with.
I agree with Troy here... look, thing is, one fuel injector is not going to be physically able to dump that much fuel in that short amount of time during vehicle operation. It's a finer detail that I overlooked in my previous postings. Those things only have a flow rate so high...
But, like he said, at cranking speed while doing a compression test, fuel does get pumped into the cylinder... but not burned. So that could be a problem.. You're supposed to pull the fuel pump relay and release line pressure before a compression test- or anything similar that disables the fuel delivery system.
He's also correct -again I didn't mention this, but it's true- if while driving down the road one or more injectors stuck open, the vehicle will see this via various sensors and pull back on fuel trim, but even still, yes, Bank 1 or Bank 2 fuel trim too rich codes will set. Possibly O2 sensor out of range codes as well.
With only two fault codes present, that we know if, and for cylinders 1 and 2... what I'd do is clear all fault codes and start the vehicle... I'd run it (possibly drive it around the block) until the MIL came back on and then immediately check DTC's (Diagnostic Trouble Codes).
With a PROPER vehicle scan tool, not some couple hundred dollar code puller that only shows vary basic data, reading actual fuel trims, injector pulse cycle data, sensor voltage outputs, etc., a GOOD technician worth his salt could figure this out with a few hours diagnostic time.
Also, I use the word "technician" on purpose. I learned this when I worked service dept at a local dealership. These guys were in advanced automotive and computer diagnostic training programs for 100 hours a year at least.. they need to know more than just how to turn a wrench, which differentiates a 21st century automotive technician from yesterday's "mechanic"...
My dad was a mechanic. he fixed mechanical things with he was a reciprocating engine mechanic with the Marines in Vietnam, later a Volkswagen mech back in the 70s. Computers and sensors and diagnostic scan tools didn't exist. The technology was different and so were the people who needed to work on these vehicles.
I say all of that to press the issue that when looking for a shop to trust with what for many of us is our second most valuable/expensive possession (other than our homes), consider exactly what the skill set and skill level is of the guy or gal who's working on your vehicle.