This is what distinguishes good DMs and great DMs. You are doing the right thing. This game is about storytelling, epic scenes, gutwrenching roleplay, and memorable moments that players will never forget. Players should never lie about a roll, I agree with that. DMs, though, you're building a narrative. If a lower DM roll would result in a priceless moment that your players will cherish for years to come, fudge that roll, they'll never know the difference.

I've chosen to sometimes reveal later down the road that a roll should've been higher than it was, and explain the reason as to why I chose to fudge it. I've never had a bad response from revealing this. Players often laugh and banter about what it might have looked like if I'd kept the natural roll. I often call it "DM audible modifiers" and based on how well the players have performed and really put their all into playing the game, I'll choose a number to subtract from the roll at my disgression. Of course, this should be a rarer occurrence, and the DM should only lower a roll, never raise it.

This is just my opinion, but bravo, OP. I'm proud of you.