That is correct. The kind of geometry that Euclid practiced (compass and ruler) was found to be in a one to one correspondence with analytic geometry (using real numbers in a plane.)
But in an Einsteinian world we learn that things are just not that perfect. due to the warping effects of gravity a triangle made of of three rays of light would not have inside angles that add up to 180.
And here is what others have said:
" ...... "
Since EG is only an approximation of reality then 2+2 is only approximately 4
due to the various effects of gravity and near speed of light phenomena in any observations.
To make it simple, suppose the non-Euclidean geometry is on the surface of a sphere of radius R. Suppose each angle of a triangle is a, b, and c. Suppose the area of the triangle is A.
According to Girard's Theorm, the sum of the angles is, 180 + area / R squared. Or, algebraically,
a+b+c = 180 + A/(RxR)
This can be interpreted to say if the radius is huge, or the triangle area is small, the sum is close to 180. This makes sense -- the triangle is small compared to the size of the sphere. E.g. a small triangle drawn in the sand on the planet Earth.
In one sense this formula is analogous to saying something like 2+2 is slightly larger than 4, but it is also gives a very explicit formula for deciding what the 2+2 actually is. That formula itself uses regular real numbers in the 2+2 = 4 sense. So the formula above is a way of relating the non-Euclidean geometry to the usual simple arithmetic properties of numbers.
If you want to think of this whole thing as 2+2 not= 4, that's fine, but a mathematician would prefer to think in terms of Girard's formula that uses arithmetic as we generally know it.
I think the discussion earlier was in terms of scientists disagreeing on what is "fact". The above discussion illustrates that people might want to look at 2+2 from two different perspectives, but understanding why and how the perspectives differ is the important factor that says the two perspectives are not in conflict.