The official US Army position is "Yes, it did happen" (But they are not specific on the type of Tiger)
From the teaching material of the US Army's Armor School back in the 1960s: https://apps.dtic.mil/dtic/tr/fulltext/u2/a952910.pdf
While the northern and eastern flanks had been heavily engaged, the northeastern sector (Troop A, 87th Cavalry Reconnaissance Squadron; Company A, 38th Armored Infantry Battalion; Troop B, 87th Cavalry Reconnaissance Squadron) had been rather quiet. The only excitement there had been when an M8 armored car from Troop B destroyed a Tiger tank. The armored car had been in a concealed position neat the boundary of Troop B, 87th Cavalry Reconnaissance Squadron and Company A, 38th Armored Infantry Battalion, when the Tiger approached the lines at right angles to move along a bail in front of the main line of resistance. As the tank passed the armored car, the latter slipped out of position and started up the trail behind the Tiger, acceleratingin an attempt to close. At the same moment the German tank commander saw the M8, and started traversing his gun to bear on it. It was a race between the Americans, who were attempting to close so that their 37mm gun would be effective on the Tiger's thin rear armor, and the Germans, who were desperately striving to bring their 88 to bear. Rapidly the M8 closed to 25 yards, and quickly pumped in three rounds; the lumbering Tiger stopped and shuddered; there was a muffled explosion, followed by flames which billowed out of the turret and engine ports, after which the armored car returned to its position.
This has led to some controversy on several grounds. One is the thought that even at point blank range, a 37mm could not penetrate a Tiger's armor anywhere. The second is that German records indicate no Tigers were in the vicinity of the battle on that date, and that even if there were a Tiger around, the nearest units were Tiger IIs, but they missed that location, according to German records, by a day or two.
However, this is not the end of it. The US Army material identifies a witness by name.
This action was reported to Major Donald P Boyer Jr, S3, 38th Armored Infantry Battalion, by Captain S. H. Anstey (Commanding Company A 38th Armored Infantry Battalion) who witnessed the engagement.
So this wasn't a case of the armored car crew claiming the kill, this was an officer from an entirely different unit who was sufficiently impressed by what he saw that took it upon himself to mention it up the line of his own chain of command. It seems reasonable to conclude that something impressive happened.
The first objection I will summarily dismiss. No matter what paper statistics say about how easily Gun A can penetrate Armor Value B, there is ample evidence to show that Gun A can still kill Tank with Armor Value B. The vagaries of life, luck, and quality control of armor and ammunition have never been told to obey the paper statistics. It would not be the only such kill: In North Africa, I have encountered a claim by a unit of M3 Light Tanks (with the same 37mm) of killing a Tiger 1, and they are very specific about it not having been a Panzer IV.
The second objection is more difficult to dismiss, as one can probably believe that units were where they were said to be. That does not preclude the possibility of a singleton having gotten lost or detached. Tanks normally do not wander around battlefields on their own (Not least, recovery if it gets stuck can be problematic), and the description of the engagement is that this one certainly had no friends or accompanying infantry. Thus is it not impossible that the vehicle killed was a Tiger II from the 501st which was driving nearby about then heading for Stavelot. The engagement was not on the correct road, but if the Tiger II suffered a temporary mechanical breakdown (Tiger IIs not being known for bullet-proof reliability), and the crew got lost trying to catch up, that would explain the singleton tank and the claim of a Tiger II.
There is a third possibility, though, that of simple mis-identification. A Pz IV can look a heck of a lot like a Tiger I, especially given how rare the latter was in US Army experience in Europe. The vast majority of cases where the US reported meeting Tigers, they were really Pz IVs. And, of course, a 37mm can certainly punch through the rear. But this still leaves open the question of "where did this singleton tank come from?" A similar argument can be made that it was a Panther and not a King Tiger, there were plenty of both rolling around the region.
The definitive answer to your question, thus, is we don't know and I doubt we ever will. We can be confident that an M8 did kill a tank at point blank range from the rear, the exact type of tank is questionable. I think, on balance of probability, it was a detached King Tiger of sSS PzAbt 501, but that's as far as I can go.