I disagree.
Dr. Gerald George has a really great breakdown of why this is in his book, Championship Gymnastics; the short version is: the stiffer the surface, the more the arms and legs should band apon impact between skills. The reason is simple -- the body's center of mass should be significantly behind the base of support on takeoff between a roundoff and a backhandspring (and between multiple backhandsprings); in most cases, this means a slight hesitation must occur between landing each skilla nd taking off for the next. The more give the tumbling surface has, the less give the gymnast's joints must provide in order to accomplish this. So if you're tumbling on a tumbletrak, there should be nearly zero bend, but on any other surface this bend is necessary, and the stiffer the surface the more bend must occur.
This is visible in most upper-level tumbling -- watch any top gymnast's roundoff-backhandspring on floor in slo-mo, and this bend will be very visible -- since the spring floor itself has a certain amount of give, the delay between skills comes partially from the tumbling surface and partially from the athlete's own body.
That said, there is another thing that will decrease the amount of bend necessary -- the athlete's ability to turn the roundoff over. However, I don't think there are many if any athletes who can get such a strong turnover as to be able to do a roundoff backhandspring on a stiffer surface than a tumbletrak without bending the knees.
This is true with saltos as well, though to a lesser extend -- if you look very closely, there is in most cases a very slight bend in the knees upon impact right before taking off on a salto, though it's much less pronounced in the case of saltos. However, just like in backhandspring series, this bend will need to be more pronounced on a harder surface.
That said, I wouldn't really worry about teaching it differently -- the gymnast will tend to make these adjustments on their own; they'll just need a few warm-up tumbling passes to get accustomed to any new tumbling surface, and most kids will make the adjustments on their own without even realizing it.
EDIT: Examples:
1) Kohei Uchimura on tumbletrak (almost zero knee bend between roundoff and backhandspring):
[youtube]4dv78x20_sM[/youtube]
2) Kohei Uchimura on floor (Much more visible bend and "jump" between roundoff and backhandspring):
[youtube]AwVzdD-07MM[/youtube]
(Skip to 1:30 if you want to see it in slow-mo)
This trend would, no doubt, continue if he were to tumble on an even harder surface, ie a non-sprung floor. He would have to bend his knees more between the roundoff and the backhandspring, making the transition more of a jump and less of a punch.