Changing your Mac address, or wearing a fake beard, are both fine.
Changing your Mac address to trick a Wi-Fi hotspot which gives out one hour free per device per day, or using a fake beard to trick a shop keeper into letting you get "one free bagel per person" twice, is a crime.
It's not illegal, it can be detected and then used against you in an indictment. It's like saying you dislike someone, they go missing, and the prosecutor mentions what you said.
And then what? You're under further suspicion? If you're innocent, that shouldn't be your concern. But all you gotta do is STFU. Don't talk to the police either way.
What you said shouldn't be enough proof except in a banana republic.
If you were always spoofing your MAC address however, then you can use that as your defense.
Your argument is akin to it being suspicious that you use Tor. As if that means your computer should be seized because you might have WMDs. Tor usage might make you suspicious only if other credible factors exist.