The key statements in the Scalia passage you quote:
"Although this provision does not state that suspension must be effected by, or authorized by, a legislative act, it has been so understood, consistent with English practice and the Clause’s placement in Article I."
"During the Civil War, Congress passed its first Act authorizing Executive suspension of the writ of habeas corpus, to the relief of those many who thought President Lincoln’s unauthorized proclamations of suspension unconstitutional."
If these are not equivocal statements, I don't know what are. Scalia hedges his bets by stating what the "understanding" is, and relates what people "thought" - without passing judgment himself.
...so claims the king of equivocation.
Returning to Scalia's dissent, though, we find that his recognition of Congress as the sole authority that may suspend Habeas Corpus is downright unequivocal regardless of what equivocation-boy says. From Scalia:
"It follows from what I have said that Hamdi is entitled to a habeas decree requiring his release unless (1) criminal proceedings are promptly brought, or (2) Congress has suspended the writ of habeas corpus."
"If the situation demands it, the Executive can ask Congress to authorize suspension of the writ–which can be made subject to whatever conditions Congress deems appropriate, including even the procedural novelties invented by the plurality today. To be sure, suspension is limited by the Constitution to cases of rebellion or invasion. But whether the attacks of September 11, 2001, constitute an “invasion,” and whether those attacks still justify suspension several years later, are questions for Congress rather than this Court."