Under the conditions as stated they could hypothesize that time is linear. However, they would really need to make the same observations under different gravitational conditions to test their hypothesis. IF they didn't realize that different gravitational conditions existed they would probably be more likely to accept the hypothesis as true.
In a somewhat similar situation it is believed that what an object is made of has no effect on how it behaves in a gravitational field. I believe there is currently a satellite in orbit, or about to be in orbit, to test whether gravity affects different materials the same way. It has samples of different metals, I forget which ones, and will see if they experience exactly the same acceleration due to gravity. Presently we assume it does, but we haven't done extremely fine tests, since they are hard to do. This test will check the idea much more precisely than has been done before.
I don't think that anyone really thinks that they will not respond precisely the same, but science is always trying to find out if what we think is true is really true.
Bill Gill
