Can Cheney say as much?
Presumably you are referring to the Vice President's deferment requests.
An interesting attempt to compare apples with oranges: let's look closer.
Ron Paul was drafted in 1962. At that time, Ron Paul was a medical resident and America was not at war. As Ron Paul himself has pointed out, his position as a flight surgeon permitted him to spend most of his time near his family and his position as a flight surgeon allowed him to continue his career uninterrupted: in point of fact, while his service as flight surgeon counted toward his medical residency it had better hours and higher pay than the civilian residencies available to him.
His service was lucrative and during peacetime.
The Vice President's number came up in 1966, while he had a pregnant wife and while he was working on his doctorate - and while the US was at war.
Unlike Paul he would have had no chance to stay near to home, nor did his civilian career give him the militarily-relevant experience to pick a plum military position safely in the rear.
Military service for Cheney would have meant putting his career on indefinite hold and leaving his wife's side while she was pregnant.
For Paul, military service meant neither of those things.
One can condemn Cheney for seeking deferment, but the historical facts show that Paul was strongly incentivized to embrace the draft, while Cheney was strongly incentivized to defer.
And all this becomes relevant in an election because Paul is running for office while he allows his supporters to scurrilously magnify his military record, as OrthodoxPresbyterian did for months, describing Paul as a "Vietnam combat flight surgeon" and falsely implying that Paul served in combat and that he served in Vietnam, neither of which was true.
The Vice President is not running for office - and while he and Paul both studiously avoided combat during Vietnam, Ron Paul figured out a way to get paid by the government to do so, while the Vice President relied on the private sector and not the taxpayer.