"[be] ready to receive any Throw that he shall think fit to give; but wait not for it, it being safer to attack than be attacked" - Thomas Page, The Use of the Broadsword, 1746 page 46
"Avoid, if possible, making the first attack against any adversary, more especially a stranger, it being advantageous to act on the defensive" - Alfred Hutton, Cold Steel page 42
In historical fencing there is obviously a spectrum between systems that favour offensive actions and systems that favour defensive actions. Much like the discussion between the merits of the point and the edge it is not a case of one approach being objectively wrong and the other objectively right but about subjective personal preference. They are both just different flavours in the rich soup of historical fencing.
However both approaches do advocate fencing “securely” which means covering/protecting yourself while you act. I've not seen any treatise that advocates attacking without any concern for your defence whatsoever. It is certainly bad practice to pursue offensive actions without training to cover yourself from your opponents defensive actions. This is the essence of “guard” positions which are ubiquitous to all treatises.
The difference is not whether you guard yourself or not but about how you use the guards. While a superficial read of treatises like Meyer might suggest that you get stuck in without concern for your safety:
"note that when you wish to fight with someone, then see that you are the first to be in place so that you can act in a timely manner in your intended piece, then you shall forcefully continue against him with cuts that he cannot send himself into a guard or piece. But rather you shall show that you will rush over him with sudden stepping before he realizes it." - Meyer, (1560) 10r
What he is actually advocating is not using “settled” defensive guarded positions but rather using guards dynamically to cover yourself while being aggressive:
“However this rhyme teaches you that it is always better to not settle into a guard. It guards you not at all, to show someone with your guard”- Meyer, (1560) 111
Or another example of this from Thomas Page:
"Advance briskly up to your Adversary under the Cover of an Outside, and Throwing an Inside but not home, receive an Outside, just sufficient to open your Adversary's Play” - Thomas Page, The Use of the Broadsword, 1746 page 38