"Symbolic-numeric" could be BS, but I'm pretty sure it's not. What might be triggering your BS alarm is the "symbolic." However this word has a precise meaning, especially in Mathematica et al's case. It basically means "replacement rules on arbitrary expressions." For example, we could define a derivative rule in this kind of way:

  x^n -> n*x^(n-1)

If you have enough of these kinds of rules and a smart infrastructure around them, you can perform sophisticated "symbolic" calculations. The whole setup is similar in essence to a Lisp macro system. As a specific example, type the following into Mathematica (or WolframAlpha):

  E^(I 2 Pi)

The result you get is "1". Not "1.000001", not "1 in floating point", but "1" as an exact symbol. So when they say they are using "symbolic-numeric" methods, what they mean is that they are using a combination of exact mathematical calculations (exact according to pure mathematics - thus invariably symbolic) in combination with numeric approximation/heuristic methods

I use Maxima daily, so I get "symbolic". I called BS because they provide no details, no citations, nothing to make me think they have advanced over Maxima, or even GCC in terms of optimization of arbitrary computations.

Perhaps more importantly, just because one can build a model does not mean one will understand the model or the system be modeled. No software will provide us with good interpretations of our models and their output.