I'm a US native English speaker, intermediate in Spanish. I don't think it's true, I think it's just linguistic pride.
I think English _is_ richer in synonyms than Spanish, because our vocabulary is drawn from two sources: one, Latin, is the same as Spanish, but the other, old English, is different. We have two vocabularies in one. As a result, we have many pairs of synonyms: an everyday, core vocabulary word from Old English and an advanced word from Latin. The Old English word is usually short, often a single syllable, while the Latin word is usually longer.
Belly and abdomen
Brain and cerebrum
Speed and velocity
Sailor and mariner
Glassy and vitreous
Bloody and sanguinary
Greasy and oleaginous
Oil and petroleum
It may be true that because we have more vowels (about 20 for English and 5 for Spanish), and because we allow consonant clusters ("strength", for example--eight letters and a single vowel), that we have more single-syllable words. To the English-speaker's ear, short words sound "punchier," strong, and more direct. That might be interpreted as "colorful." Compare "The ship fought the storm and the high waves for hours, and arrived safe in port" with "El barco luchó durante horas contra la tormenta y el fuerte oleaje y llegó sano y salvo a puerto." 17 syllables versus 33.
English is an ugly language for singing, though. Spanish (and Italian!) are better for singing because of the wide, clear, open, beautiful vowel sounds, while English is full of muddy, closed, in-between vowel sounds that don't sing well.