Plus or minus 10% is the same as being 20% off. (eg 10% higher plus 10% lower = 20% off)
The FDA rules are such that meters can read 20% higher or 20% lower. It's not 20% in total.....it's actually 40% overall using your math.
Meter readings are not an exact measurement and neither are lab values for that matter. BG is a constantly changing entity so if you test twice with the same meter or lab equipment even on the same drop of blood, chances are the readings will not be precisely the same. I agree with your vet about the meter variance not only by brand but also same meter, same brand. Some meters will be more accurate at low ranges, some at moderate ranges, and some across the board etc. but all must conform to the regulations set out by the government health agencies as far as variances are concerned.
Some meters will error out if the sample is too small, some won't read at all if the sample is too small and some will give you false readings. It's important to know how your particular meter functions in those situations. When a low number is encountered, it's a good idea to double check it. I see nothing wrong with comparing your meter with the vet's lab results to get a "feel" for how different the readings are BUT when dealing with low readings on a human meter, I don't see any positive value in trying to assume what that number means in lab values before taking action. There is a bluffer built into the human meter references given here so whether my meter reads 2 or 10 points different than the lab values, doesn't matter to me. At 50 on a human meter I am going to take action because I have no way of knowing if that reading really is 40 or 60. If I make the assumption it's 60 and take no action and it's really 40, I am putting my cat into serious danger.
All sorts of things can effect the results from glucometers. Expired strips, bad strips, low battery power, temperature, sample contamination etc. Manufacturers generally recommend checking the meter using test solution each time a new vial of strips is started to ensure the strips and meter are functioning properly. If you follow this advice, and ensure the sample is not contaminated by washing your hands before testing, you can be pretty confident that your meter is functioning correctly and trust the readings using the appropriate reference numbers without questioning them. If at some point you suddenly get an unexpected reading, double checking is advisable.