In general, the advice not to cross strains is good advice. It would be a good way for a beginner to wreck a line. Not to mention that there is some value in the integrity of a good line or strain.
That is not to say that there is not occasion to do the contrary. On occasion, there is. One example is the strain that most have here. They are more than the result of crossed strains. They are the result of crossed breeds.
I would agree that it is worth mentioning that no new beginner should cross strains for the sake of improving "genetics" (I do not know what improving genetics means.), or a concern with "genetic diversity". How can we tell if they are too inbred if they have not even been raised up, and the next generation grown out?
Most of the good breeders will bring something new in (even unrelated), at some point. It is possible to breed them too close. It is also possible that a particular characteristic needed for improvement is not available in the existing line or strain. If the characteristic is strong in a different line of the same strain, then all is well. Otherwise, a breeder may decide that crossing strains is necessary to move forward.
Then it is done cautiously. Anyone that has worked with something a period of time, and has made consistent progress does not want to risk their work to the unknowns. It is commonly recommended to introduce the new bird on the female side, using one of your own males in an initial side mating. Then adding a pullet or two to a family etc. This hypothetical or some other variation of it is based on emphasizing caution, and limiting the influence of the new bird. Preserving the integrity of the original line.
A flock that needs radical improvement might be better off with using a new male if one could be had that is from a much better background.
With the above scenario, it is still important to advise new people not to cross strains. Especially if what they have is of any quality. It takes multiple generations for anyone to get to know what they have, and that is especially true for someone that is only beginning to know what they are even looking at. A haphazard cross is blasphemy to some because it almost guarantees poor results, and years of breeding out "the bad again". It may be one of the fastest and surest ways to ruin a good line in the hands of a beginner. For those of us that are beginners, we always think we know more than we do. Always. It is not always what we do know that gets us into trouble. It is what we do not know, and we cannot know what that is until we do.
We cannot possibly know what a line needs, or what variability there is to select from until we have grown out multiple generations. So why even bother with the idea of crossing strains until you have been convinced by the evidence that it is necessary? Some one new should instead focus on learning the art of selection, and working on improving what they already have.
Bob's, and other's advice, that went along with this was to stay away from anything that was not already in good shape. His advice was based on the idea that the quality of the hypothetical flock was very high. Reconstruction efforts are another topic all together. Bob recommended potential new breeders to stay away from such projects, and this to, was good advice.
To the mention of brother/sister mating. It is not as taboo as some make it out to be. It might instead be considered a tool. Initially the offspring will be no more inbred than a father/daughter mating etc. In a line that is already very close, the results would obviously be different than one that was not. Occasionally, one might want to repeat a brother sister mating in order to "set" particular characteristics in a new line. Of course, continually repeating the mating, or in a line that is already too inbred could result in some unhealthy recessives. It would not be considered normal practice, but there might be an occasion where it is acceptable, or even advisable.
Along the way, new breeders learn when to do something, and when not to do something.
In the beginning, just forget about crossing strains and learn to work with what you have. That is after you have purchased the best possible birds you could come up with. Don't throw possibly decades of some one else's work down the drain just because it seams like a good idea. 3, 5, years from now you will know better about what to do. Any decision has to be intelligent, calculated, intentional, and cautious. A lot of time, work, money, thought, and feed has went in to some lines. There is a lot at stake.