This is an inherently tough situation for the founders but not unwinnable, provided:
1. The code is as they say it is, entirely independently developed as opposed to code that infringes the employer's copyright because it has been stolen.
2. No moonlighting took place. If it did, the IP is so related in its broad subject matter that, even under the liberal California law, it could be said that it involved a reasonably anticipated extension of the employer's existing products or IP development, in which case it would belong to the employer even if the employees developed it strictly on their own time and strictly using their own resources while employed.
3. The Shred products do not embody proprietary trade secret information belonging to the former employer. For the employer to have a legitimate claim on this prong, it would have to show that it had non-public information (e.g., special algorithms, techniques, etc.) that gave it a decided competitive advantage, that were not known to others in the field, and that were the subject of special efforts by the employer to keep them confidential. If an employee who is bound by a typical confidentiality agreement learns of such trade secret information or techniques only while employed, or even develops or discovers them while being paid by the employer, all such trade secrets belong exclusively to the employer, even if the employee is capable of walking away with the secrets "in his head" only. If, however, the techniques, insights, information, etc. that the employee later used to develop the new products following termination of employment consisted of things known or derivable by any person skilled in the field were derived exclusively using that person's general skills and expertise, and not from taking any employer's proprietary information, then the employer has no claim on any of this. In particular, if someone was already an expert in the field before beginning the employment, and applies what he knows for the benefit of his employer while employed, that employee continues to own what he came in with and can use it as he likes in any post-employment situation. He does not lose what is his just because he passes through a particular employment situation. So, summing up, if the post-employment products derive exclusively or primarily from a former employer's "secret sauce," the employer has a claim; if they derive only from the general skill and expertise of an employee, the employer has no claim.
4. Nothing in the new products infringes any patent belonging to the former employer.
5. No other acts of unfair competition took place that would have tainted the new venture (e.g., no raiding of other employees by soliciting them while employed, no post-employment violation of any express non-solicitation clause, no customer theft based on misappropriation of trade secret information and the like).
6. The founders have a practical way of dealing with the legal costs and the impact of the lawsuit cloud on their ability to develop as a company. If the case is a clean one from their perspective, this usually means the employer will not be able to get any type of preliminary injunction to stop the venture during the legal fight. In that case, if the new venture can generate revenue, this can help fund things or can possibly be sufficient to assuage concerns of investors so as to convince them it is worth their while to fund the venture in spite of the lawsuit. The dollars involved in such a defense are large for a small venture but can be managed in the right situations (likely in the hundreds of thousands, more if the employer is particularly obnoxious).
7. If the former employer is taking a reputational hit by pursuing the lawsuit, this works in favor of the founders as well because there is a real price to pay besides money for being a bully (if that is what is happening). After all, who wants to work for a horse's ass of an employer given a choice.
I don't know the facts here but there are several indicators that the Shred founders are being truthful in what they are saying. If this all followed from an initial rejection of the former employer's effort to own or control them, this likely indicates bad faith by the employer. The offer to have the code compared by a neutral is also important. It is true that stolen code by itself may not be the key thing but such an examination can bring to light many important things about whether a viable claim exists here or not. The employer's apparent refusal to allow this does not speak well of its motives. Even worse, if, as I understand it from public reports, the employer wants the code turned over to it in discovery, this is a very bad sign. Even if this is done under a so-called protective order, this sort of tactic is very often a tip-off that it is the employer and not the employees that is trying to engage in dirty tactics to gain a competitive advantage. Information is very amorphous and having the employer's developers scour the code directly is a sure way for them to grab key ideas/techniques that they normally would have no ability to access. Another tip-off is the employer's CEO being taped making statements that he intends to win whether the employer is in the right or not. By itself, perhaps an inconclusive statement but combined with the other factors, this does not look like good faith. Finally, YC is standing behind Shred. This, again, is only an indicator but YC has demonstrated itself to be nothing if not honorable in innumerable situations and it does not want the taint of being associated with a dirty company. Its support is thus a good indicator of what is going on here in reality.
Only time will tell who is right but, on the surface, this looks to me like a classic case of abusive litigation aimed at gaining something besides a just result on the merits.