Sean,
You asked, "Somebody recently told me that the Canadian v USA cricket match with Tilly on board was the first international team match of any sort that is recorded in history. Does anybody know if there is any truth to this?"
I don't believe this is so. I believe that the person who told you this may have been confused with what happened in a few different events that Tilly was involved in. Here is my reasoning.
The date for the CRICKET match in which Tilly played against Lyon is unknown to all of his family members and I have never been able to find any records for it other than the article in which Tilly made mention. Without a date, how can anyone claim it as the first? It probably occurred before 1895, as this was the year of his first trip to Scotland. That trip ignited his passion for golf as almost nothing else would throughout his entire life. The only thing that would stoke the flames of this passion even higher was his second trip over to St. Andrews in 1898. He came back from this one and designed his first golf course in Frankford, Pa. From this time onward, Golf was everything to him.
We know that he was playing Cricket as early as 1892. But his playing in a "first international match" in cricket before this time is problematic because of his age. He was born on May 7th of 1876, and in the summer of 1892 was ONLY 16 years old. It would seem than that his match in which he played against seems to most likely to have been played between 1893 to 1895. Still, it appears that this is another sport at which Tilly was very talented. The photo of him with his team in 1892 shows him in the center and this hints at his being among the better players. Also, his moustache is pretty strong and one would guess at an age of at least the early 20's for him. The problem is that the photo has a date of 1892 on it placed there by his wife, Lillian. Could she have been wrong when she dated it? There's no way of telling.
So the date for his match is unknown.
Secondly, Tilly wrote an article that appeared in the June 1933 issue of Golf Illustrated titled, "The First International." It may be this occasion that your friend was thinking about. This was the "first encounter between teams of golfers representing England and America. Previous to this there had been team matches between the United States and Canada [all played in the U.S.], but 1903 marked the first crossing of the ocean for the meeting of teams of two continents."
I believe it is this match that he is refering to. J.L. Low captained a team from the Oxford and Cambridge Golfing Society that took on teams representing diferent U.S. cities in a series of matches. Among the courses they were played on were Garden City, Huntingdon Valley and Atlantic City. Tilly played on the Philadelphia team and appeared to have attended all of the matches himself.
By the way, among those who were on the Oxford team - C.H. Alison, who would go on to do, as tilly himself wrote, "some extremely meritorious work as a golf course architect."
Finally, as for any of these matches being the "first international team match of any sort that is recorded in history," I believe that the America's Cup yachting matches go back quite a bit further and that this is the first organized international competition, though I could be wrong in this.