I'll have to say that you are right, since Congress went along with it.
If Presidents have the power to suspend habeas corpus, why did Congress specifically authorize Lincoln to do so later in the war? Answer: Lincoln didn't have the right, and Congress recognized that he didn't.
Congress was not doubt aware of Chief Justice John Marshall's words in Ex parte Bollman and Swartwout: "If at any time, the public safety should require the suspension of the powers vested by this act in the courts of the United States [i.e., the power of awarding the writ], it is for the legislature to say so. That question depends on political considerations, on which the legislature is to decide; until the legislative will be expressed, this court can only see its duty, and must obey the laws."
From what I have seen Congress did not go along with it until two years after the fact in 1863. Lincoln's original suspension of the writ was in 1861 when Congress was out of session. Had he desired to suspend it constitutionally he would have had to call Congress back in session and ask them to do it first. He did not and instead acted alone. The ensuing arrests were immediately challenged in at least two federal courts: the U.S. District Court in St. Louis and the U.S. Circuit Court in Baltimore. Both courts ruled against Lincoln. The St. Louis court order was obeyed by the general in command there for the one particular prisoner but ignored for everything else. The Baltimore court order was ignored by Lincoln entirely. In any other time of our history what Lincoln did - ignoring a federal court order for no other reason than not liking the outcome - would be an impeachable offense.