Dial print quality New Seamaster

Even with a warranty card, there’s no guarantee the watch is authentic, and the serial number would indicate the date if needed.
This is just to steer people away from dealers who are not obligated to follow Omega pricing guidelines, etc.

Omega are admitting nothing of the sort. The response to the OP states that "OMEGA watches purchased from unauthorized sources may be damaged or counterfeited ", in other words unathorised dealers may be selling counterfeit watches or watches that have been damaged before the unauthorised dealer got them. First, Omega does not make or supply counterfeits. Second, in my experience authorised dealers will have watches that have been tried on hundreds of times and have been mishandled by the customers or the staff and have dinks, scratches and even gouges in the case, bracelets or crystals. It is these watches that Omega seems to be referring to. I have rejected several watches in the past at authorised dealers because there have been marks and dents on the case and the dealers just order brand new ones from Omega. Usually these "shop soiled" watches get sold in the annual sale or sent to head office and moved onto secondary market dealers. Only once did I go ahead with a purchase of a scratched watch but only because the watch was a discontinued model so no brand new unmarked replacement was available and the dealer knocked a chunk of change off the price. The watch was then sent away to Omega for a refurbishment and came back like new. Although I could not wear it for a few weeks while Omega restored it the discount was more than enough compensation for that inconvenience

Omega Boutiques always fill in and stamp the International Warranty Card at the point of sale. I generally do not buy watches from an authorised dealers/jewellery chainstores but having done it a couple of times over the years they also fill out and stamp the Warranty Card at the point of sale. Any seller stating "it is all done online" is lying and diminishing the value of the watch you have just bought. i would probably tell them the sale is off and get my money back if they tried such behaviour with me. I would also contact the Omega head office in my country and give them the details of the problem. Omega are actually quite happy to take dealers to task over this sort of thing.

For the record, regarding quality control (and @Archer can weigh in better, I suspect): all companies have a specific standard about how the watch should look. A close friend is Omega certified and I'm fairly certain Omega's standard is that a watch passes quality control if, from 12" away, there are no visible abnormalities. This watchmaker friend has all sorts of stories (as does every watchmaker I know) about customers upset because of a tiny speck that can only be seen under magnification, and, while he generally will solve those issues, he makes sure to explain that the actual Omega standard is 12" with the naked eye—meaning, sure, very small specks might exist, but they do pass Omega's established QC.