Not quite. 300w speakers on a 300w amp can definitely blow. A 300w amp driven to clipping will be more harmful than a clean, unclipped 500-600w amp any day.
You can definitely overpower speakers safely, too. I’ve done it for years. Power ratings are a warranty thing, not a definite. The gain is your friend.
Only pay attention to RMS ratings as well… Peak power is bullshit. Generally, most higher end companies will state it as twice RMS power… in many cheaper brands they will state it as 3x to 4x RMS power. It’s marketing bullshit.