Except, all its rulings are reviewable by the courts. In judicial type cases, results can be reviewed by US Court of Appeals, and appeals courts do overrule the NLRB not infrequently. Rule making is reviewed by courts under the Administrative Procedure Act. This has been standard in the US court system historically for administrative actions at all levels, from school boards making the rules and also deciding cases involving employees and students, to the FDA and SEC for example.

Also the president has always had some power to remove board members for cause, not Congress. Congress can change the enabling statutes but only if the President signs the law (or they override the President's Veto). I'm not aware of how Congress can intercede in specific cases.

So I don't think it's actually so that the NLRB not answerable to anything but Congress.