They're technically not wrong. Germany did not sign a peace treaty at the end of World War II but that does not mean that a state of war persists. A war can be ended in several different ways, a peace treaty being one of them. Now, in the case of the German surrender of World War II, there are two ways we can look at the German Instrument of Surrender.

One way would be as an unconditional surrender in which all German armed forces laid down arms. This too is a cessation of hostilities and effectively leaving the dictation terms for the peace treaty to the victorious party. Effectively, peace dictated by the enemy but peace none the less.

Another way to look at the cessation of hostilities in World War II is as a modern case of debellatio. This term means, in essence, that one party of a conflict has been completely destroyed, no sovereign territory remains under their control. The Roman conquest of Carthage in the Third Punic war in the second century ended debellatio. Carthage ceased to exist as a nation. One could argue that World War II in the case of Germany also ended debellatio, no sovereign German territory remained.

The German state effectively ceased to exist as an entity. This would effectively void a debate as to whether or not Germany surrendered or signed a peace treaty as Germany no longer existed. The modern day Germany is a separate entity from the Germany that ceased existed prior to the the surrender of World War II.

As to the second question of Germany still being occupied, this is just silly. Simply because foreign national troops are within a nations borders does not make it occupied territory. The occupation of western Germany ended 5 May 1955 with the implementation of the General Treaty which formally ended the occupation. The remaining restrictions under the General Treaty were in turn removed in 1990 with the reunification of Germany. There is no argument here. Germany is a sovereign state by every definition of the phrase since 1990.

The U.S. Army in the occupation of Germany 1944–1946 - Earl F Ziemke

The Laws and Customs of War on Land - 4th Hague Convention

Unconditional Surrender: The Impact of the Casablanca Policy upon World War II - Anne Armstrong

EDIT - Third Punic war, Second century. Not the other way around.

This one is a mixture of true and false. They broadly have a point however it is basically false. What happened is that a settlement was made without Germany participating and was given to Germany as a communique in 1945 however this was only a temporary. The exact quote in the communique is as follows " a peace settlement for Germany to be accepted by the Government of Germany when a government adequate for the purpose is established" Now this agreement even if it was not officially a peace treaty served the purpose well. As for when am actual treaty was signed you had to wait until 1990 and the 2+4 Agreement when the allies signed a document that was also signed by the two Germany's that agreed with the original communique setting up the boundaries of United Germany. Now again this is only on a most technical level not a peace treaty but was accepted as such by Germany,France,UK,USA,USSR. So for a tldr. Technically they are correct but by all other indicatations a peace treaty was either done in 1945,1947 (When all German allies signed a peace treaty) or 1990