For instance, let's say Frank Sinatra's "Learnin' the Blues" was America's most-played song of July 1955. Would that mean if I time-travelled to July 1955 and asked a random person if they'd heard it, they'd probably say yes, regardless of where in the U.S. they lived?
The exact formula of the Billboard Top 100 chart, which aims to list the most popular songs of a given week, has always been to some extent a trade secret. But the chart was traditionally compiled based on a combination of different ways in which people might have listened to the record, including jukebox plays, sales of physical stock, and radio airplay, once upon a time; these days, radio airplay still counts, but there's (practically) no physical singles any more, just data from streaming services and downloads from iTunes and the like. Not every national chart has always done it like Billboard - British and Australian charts have traditionally based their charts completely from sales, for example.
Google Books has a selection of old editions of Billboard available, including issues from July 1955 (for example, the July 23rd edition) (Billboard was, and still is, a trade magazine, designed to provide useful information to people in the music industry). July 1955 is shortly before Billboard had a Top 100, actually (that started in November 1955); instead, in July 1955, Billboard has a sort of top 30 in the Billboard Music Popularity Charts Honor Roll Of Hits. Generally, the most popular song of Billboard's July 23rd, 1955 edition appears to have been was 'Rock Around The Clock', with 'Learnin' The Blues' at #4. Note that I don't say 'Learnin' The Blues' by Frank Sinatra here - it was the song not the recording that the chart was measuring.
Billboard in 1955 also reported specific charts: according to Billboard's July 23rd, 1955 edition, Bill Haley's version of 'Rock Around The Clock' was #1 with Sinatra's 'Learnin' The Blues' at #2 on both the sales and most played by disk jockeys charts, with Bill Haley's 'Rock Around The Clock' at #2 on the most played on jukeboxes (with Sinatra's 'Learnin' The Blues' at #4). The reason that 'Learnin' The Blues' wasn't on the overall charts at #2 despite being at #2 in two of the three charts was specific that there were two songs which had multiple versions on the charts at the same time - 'Unchained Melody' and 'Cherry Pink And Apple Blossom White' - the multiple versions by different recording artists all counted together on Billboard's top 30 chart. It was only with the advent of the Top 100 in November 1955 that Billboard counted different versions of a song separately.
In 1955, Billboard also reported regional sales, but not regional radio airplay. Billboard say that they did weekly surveys of disk jockeys as to what they played, though they give no indication of how many disk jockeys they talked to. In contrast, with regional sales, they report separate figures from Atlanta, Baltimore/Washinton, Boston, Buffalo, Chicago, Cincinnati, Cleveland, Dallas/Fort Worth, Denver, Detroit, Kansas City, LA, Milwaukee, Minneapolis/St Paul, New Orleans, New York, Philadelphia, Pittsburgh, St Louis, San Francisco, Seattle, and Toronto. In these charts, in 1955, 'Learnin' The Blues' seemed particularly popular in Atlanta and Detroit, where it was #1; 'Rock Around The Clock' was unusually low on the charts in Detroit (#9), Kansas City (#4) and Buffalo (#6), while in Atlanta it didn't make the top 7. With 'Learnin' The Blues', it didn't feature on the charts in Baltimore/Washington, Minneapolis/St. Paul, Philadelphia, Cleveland, or Kansas City. I don't see obvious demographic similarities explaining why it was popular that week in one city and not another - to some extent it's just a crapshoot, dependent on whether a DJ might like a song or not, or on how accurate to the demographics of the whole city the record stores giving information to Billboard actually were (Billboard relied on tabulations from record stores until 1990, when they introduced a point of sales device called Soundcheck, data from which showed that its previous chart tabulations leaned towards adult-oriented-rock much more than actual sales did). Broadly speaking, the demographics of these charts clearly skewed towards large urban centres rather than rural regions, too - perhaps that July 1955 chart would have featured contemporary country hits like Porter Wagoner's 'Satisfied Mind' otherwise.
The rise of television and especially national music-focused shows like Bandstand or variety shows like The Ed Sullivan Show would come to change this, but well in the 1960s and even in the 1970s, you would get local bands who would have a regional success with a single, but who didn't break into mainstream popularity across the country. For example, many of the early 1960s surf bands like Dick Dale and the Del Tones did very well in California, and...less well in states where surfing was several hundred miles away. Beach Boys biographies typically talk of their strategy of releasing double A-side vinyl singles, where one side of the single was a 'car' and one side was a 'surfing' song - e.g., 'Surfin' USA' was backed with 'Shut Down' (about drag racing) - in the belief that inland areas of the US would be more enthusiastic about songs about automobiles, while coastal areas would be more enthusiastic about surfing. Later on, Bob Seger spent much of the early 1970s being very popular in the midwest, but unable to break through to national acclaim until the success of his 1976 album Night Moves; Billboard in 1975 no longer reported regional sales (though they then reported popular radio songs in different regions), but 'Katmandu' by Bob Seger reached #46 in 1975 nationally, but likely did significantly better in areas like Detroit and Cleveland.
So all of this likely indeed means that hits were much more regionally based in 1955 than they would be today (though there are still regional variations) and that it would have been possible - especially in Kansas City, seemingly! - to have not heard either 'Learnin' The Blues' or 'Rock Around The Clock'. It should be said that the rise of conglomerates like Clear Channel in the 1990s in particular meant that a small amount of onwers came to own a wide swathe of radio stations across the country and standardised their programming to a greater extent than in the 1950s.
Additionally, it should be pointed out that there were a variety of different radio stations and indeed different radio programs catering to music fans of different tastes; by the mid-1950s there were a variety of different stations specialising in country music or rhythm & blues or jazz or (insert genre here). In terms of mainstream pop, different stations would serve a youth pop audience more keen on listening to Elvis compared to a more middle-of-the-road adult popular music audience more keen on listening to Sinatra. So it was perfectly possible to be in one demographic and never hear music designed for other demographics, as it is today (see, for example, the confusion of R&B/hip-hop fans when the indie act Bon Iver won Grammys in 2012 despite having never previously been on their radar).
Additionally, the Billboard charts smooth things out more than the UK or Australian charts, but you do get cases where a song might sell bucketloads while being barely played on the radio, where the smaller amount of people who hear it on the radio are much more likely to buy it. Similarly, you get situations where a song is a pleasant-enough tune to hear on the radio, and so nobody changes the channel when it's on, but nobody's particularly enthused about the song either. In both cases, with the Billboard charts, those songs get on the charts, while either not being heard by that many people, or not being actively loved by that many people.