This is not how Putin works. He is quite brazenly capable of lying about something while there's evidence for it. Look at the Crimean invasion, where he baldly lied about the presence of Russian troops. Or the Russian made nerve gas used in the UK, which there really is no way a random person could have gotten their hands on. Putin even threatened them directly!

For Putin, not even having to be subtle about it is part of his power play. He likes to troll his enemies, and putting Trump up there on stage openly fawning was Putin's way of baldly stating that he holds his balls, and there's nothing anyone can do about it.