From 1960 to the present the VIN sequence number is XXXXX on the passenger side of the engine block. If your block has the CS or CR suffix and the last six of vin that matches the vin on the car, That proves it is a fuel injection corvette and is numbers matching.
Anyone telling you that you don't have the fuel injected body is probably just jealous of what you have and trying to devalue it with a con to buy it cheaper than what it is truly worth. They are basically saying your body has been replaced or the fuel injection emblems are not in the right place or missing. There is no difference in the body itself. Replacement body's are available. What makes your car what it is, is the engine itself.
Here is more information:
1961 Corvette Fuelie Show Condition Fresh Frame Off Restoration Silver/Red
The front of the 1961 Corvette looked like the 1958, 1959 and 1960 models. But the rear was restyled with four round tail lights, which became a Corvette trademark.
The wheelbase of the 1961 Corvette was 102 inches. The overall length from bumper to bumper was 177.2 inches. The height from top of the roof to road was 51.6 inches and the overall width was72.8 inches. The 1961 Corvette weighed 3,035 pounds and the fuel tank held 16.4 gallons of gasoline.
The base engine was a 283-cubic-inch V-8 that had a four-barrel carburetor and an output of 230 horsepower and a compression ratio of 9.5:1. A 245-horsepower 283 engine with two four-barrel carburetors and a 9.5:1 compression ratio was available for $150.65 extra. The same setup with 270 horsepower and a high-lift camshaft cost another $182.95. Two more 283 engines with 275 or 315 horsepower and fuel injection instead of carburetors cost $484.20 extra each.
The base price of the 1961 Corvette was $3,934, but there were many options available that would drive up the price. Powerglide automatic transmission cost $199.10 extra, while a four-speed manual transmission cost $188.30 extra over the basic three-speed manual. Power windows were $59.20 extra and a signal-seeking AM radio would set you back $137.75. A power-operated convertible top cost $161.40, while a fiberglass hardtop was $236.75. Wide white-wall tires cost $31.55 more than the standard black walls. A heater was an extra $102.25. A two-tone paint treatment cost another $16.15. A Positraction limited-slip differential was $43.05. Heavy duty brakes and suspension cost $333.60 extra.