I've heard this several times and at first it seems to hold up after the British realised the importance of the navy to defend the island. On the other hand the defeat of the English Armada a year later suggets otherwise.
You are absolutely correct to question this assertion, as you said an easy counter-example is the failure of the English Armada just a year after the failure of the Spanish Armada.
I cite a bit of background that I wrote about here.
In the first half of the 1500s, Henry VIII Tudor was allied with Charles V of Spain, and his first wife was Catherine of Aragon, sister of Charles V. Henry had wanted to marry his first daughter Mary to Charles V, although Charles married a Portuguese bride with larger dowry. Instead, Mary was married to Philip II of Spain. This was part of Charles V's grand strategy of a northern orbit: Spain - England - Low Countries.
The period of Mary's rule of England saw Spanish naval knowledge being absorbed by English shipbuilders. Mary ordered the building of race-built galleons following Spanish design but with emphasis on gunnery. This includes more guns and better reloading mechanisms, in particular re-design of the gun carriages to use 4 wheels. So basically while the vessels were designed in Spanish style, the armament was done in English style.
Elizabeth, as we know now, was a Protestant and eventually led England away from Spain's orbit to become an outright adversary. She ordered further ships built following the design done in the era of Mary. These are the ships that led the battle against the Spanish Armada in 1588.
Speaking of which, the Spanish came into that battle first of all wanting to avoid confrontation with the English fleet. Their objective was to escort a large flotilla of transport vessels to the Low Countries where they could take the Army of Flanders across the strait to England, to conquer England. And this they nearly succeeded in doing, except for weather, English gunnery, and English persistence.
The two navies had very different goals. The Spanish would have much preferred to avoid the English navy. But they had to stay together as a fleet to protect the slow and vulnerable transports. If they had to fight, they preferred to fight on the decks, not from a distance. The English wanted to stop the invasion. They didn't want to fight a boarding action, they preferred ranged gunnery action.
The Mediterranean had taught the Spanish how to fight as a navy, culminating in their victory in Lepanto. But that style of fighting failed in the battle against England due to asymmetric objectives, advances in gunnery, differences between Mediterranean and Channel conditions, poor high-level strategy (most agree that the Spanish will likely have done better if they had either invaded England or Ireland straight from Spain itself, or have the Army of Flanders do their own crossing, rather than have to escort transporters literally around England first), weather, tactics, etc.
Regardless, the failure of the Spanish Armada meant that Spain/Portugal's place as the pre-eminent global naval power was challenged by both the British and the Dutch. Further, the failure to defeat Britain meant the Spanish/Portuguese union had to bear a heavy cost in defending their colonial interests everywhere. This was the calculus that led Philip II to embark on the effort to subjugate Britain at home, because it would have been cheaper than building forts everywhere needed, and navies to patrol all the seas.
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