Regardless, they're not right - and although it's usually wise to set more in store by reliable sources, that shouldn't stop us from discussing ideas that come from unreliable ones, or simply out of somebody's head - there's no need to appeal to a better textbook to show that there is evidence of that sort. It's actually quite possible to watch evolution happening on a human timescale if you look at creatures with short lifespans. One famous and (I think) interesting example is the
peppered moth. Originally mostly white in colour, people started finding black peppered moths around 1810 - when the soot produced by burning coal was turning many trees black - and the population as a whole became darker over the next few decades, with black moths eventually becoming the largest group. The changes in tree colours gave a competitive advantage to black moths, which now had better camouflage, and the population changed as a result.
A less pleasant example is the reason why you're told to carry through a course of antibiotics even if you feel better before finishing it - if you don't, some bacteria with slightly less susceptibility may survive, though their total numbers will be too small to make you feel ill. However, these will then breed, with the result that you end up being made sick by a population that is much better at surviving antibiotics than normal, and which may prove totally impossible to reduce with antibiotics enough that it can't recover its numbers. Another is the way in which plant and animal breeders control incentives (by controlling which animals are allowed to mate, which plants are allowed to cross-pollinate, and so on) in order to produce the characteristics that they want - selective breeding, which is the reason that chickens and bulldogs don't look like any sensible animal that you might find in the wild, wouldn't exist if the principle of natural selection wasn't sound enough to make a living betting on it.
In both cases you have observations - in the former case, that trees changed colour, and the moths also changed colour within a few decades, and in the latter that a patient can take most of a course of antibiotics, start feeling better, stop taking the drugs, and soon become sick again but find the antibiotics unhelpful. Both are explained by the suggested rule that sometimes, when an organism reproduces, an error or mutation is inserted into its DNA, and that organisms which find themselves with mutations that give them an advantage in their environments have more children and so pass that mutation on, eventually displacing those who do not have that mutation. One could imagine evidence - for example, a species of black moths, living in black trees, that became white over a few generations although the trees stayed black - that might challenge this rule, and invite us to modify it (as Richard Dawkins spends most of his actually biological books trying to do) or get rid of it altogether.
To give a similar example going back to gravity, the current rule that we work on - that objects with mass exert a force on other objects with mass, which attracts the two together - isn't a million miles away, in everyday application, from Aristotle's rule that 'everything tries to get back to its natural place'. It's a question of being less wrong, or more accurately being able to predict the outcome of a future experiment with greater accuracy. For example, Aristotle would have struggled to explain how a rocket can be attracted to the Earth until it enters outer space, where it seems to be attracted (in meaningful terms) by nothing at all, until it nears the moon and becomes attracted by that. However, if you want to explain why everyday objects on Earth act as they do, you won't go far wrong if you say 'the arrow drops because it wants to reach the ground' rather than 'the arrow drops because the Earth exerts a force on it'.