That would have entailed the helo going outside the lateral limits of the route, which brings up other issues. As long as the helo is in the route, other traffic knows to look for low-flying aircraft there. Keep in mind the helo can also descend or hover.
The rules are pretty simple: listen to ATC, actually get eyes on what ATC is telling you is out there, and don't hit it. ATC has the responsibility to advise one or both pilots if the aircraft flight paths seem to merge. This was done. Based on what we know now, and accepting the hypothesis that the helo pilot mistook a trailing airplane for the one he was supposed to stay separate from, I would imaging that the approvals for visual separation may include additional requirements for "report traffic in sight," such as confirming range, distance, and relative bearing.
I haven't seen an NTSB briefing posted for today. During briefing 3, there was some comment on a TCAS voice warning that is heard on the CVR of the airliner. TCAS will not issue a resolution advisory below 1000 feet, but it will issue a "traffic, traffic" voice warning when it detects a potential collision.
If I were flying any sort of an aircraft and missed an airliner by only 200 feet vertical separation, I would be puckering as hard as it's possible to pucker.