Popa: That may well be the case for a number of reasons.
1. As you pointed out, there may be an implicit tenai in this country that when Jews act in the public sphere they act and expect others to act on the basis of Federal and applicable State law. Were it gets really fuzzy is how far you take the implicit tenai. In the case of bankruptcy it isn’t too hard to conclude (as many poskim have) that when a Jewish lender formally extends credit to another Jew he does so expecting to be bound by bankruptcy laws and those laws are halachicly incorporated into the agreement between the borrower and lender. The same would be true for many other cases were individuals enter voluntary commercial relationships. It gets more complicated when those relationships are not voluntary or result from chance or the unilateral action of one party. For example, what about tort cases; do parties go about life conducting themselves expecting to be subject to american law or halacha in these areas. A less likely case is the one posed by the OP with respect to business competition; a Jewish merchant might expect that another Jew won’t open a competing store down the block, but he certainly opened his business expecting that a non-Jew might do so. Does that change the calculus?
2. A more expansive justification would be a general reliance on minhag hamedina. If people (that includes the non-Jewish population) entering commercial relationships generally accept certain norms (provided by secular law), the minhag hamakom might bind Jewish relationships too, sometimes even if the parties stipulate otherwise. The applicability of minhag hamakon is limited, however, to cases were halacha recognizes that the intentions and mindsets of the parties control the terms of the relationship.
Of course, none of this says anything about using arkaos to enforce secular law; its really about whether, if you go to a good beis din, the beis din will be applying local law to decide the case, or will resort to the default rules in shulchan aruch.